1 edition of Low-dimensional and symplectic topology found in the catalog.
Low-dimensional and symplectic topology
Georgia International Topology Conference (2009 University of Georgia)
|Statement||Michael Usher, editor|
|Series||Proceedings of symposia in pure mathematics -- v. 82, Proceedings of symposia in pure mathematics -- v. 82.|
|Contributions||Usher, Michael, 1978-|
|LC Classifications||QA612.14 .G46 2009|
|The Physical Object|
|Pagination||ix, 228 p. :|
|Number of Pages||228|
|LC Control Number||2011025453|
Topology is the study of shapes and spaces. What happens if one allows geometric objects to be stretched or squeezed but not broken? In fact there’s quite a bit of structure in what remains, which is the principal subject of study in topology. The modern field of topology draws from a diverse collection of core areas of mathematics. Much of basic topology is most profitably. Detecting tightness via open book decompositions Geometry & Topology Monographs 19 (), Abstract: This article is an expository overview of work by the author characterizing tightness of a closed contact 3-manifold in terms of arbitrary open book decompositions thereof. The intent is to provide a `user's guide' of the theory. Title: Cotangent Bundles of Open 4-manifolds Program: Symplectic and Contact Geometry and Connections to Low-Dimensional Topology Speaker: Adam Knapp, Columbia University Date: Thursday, Novem Time: pm – pm Place: Seminar Room , Simons Center Abstract: Using results of Eliashberg and Cieliebak, I show that: if X1 and X2 are two homeomorphic open 4 . Research: My main research interests are low dimensional topology, symplectic and contact geometry and topology, symplectic cohomology. Koszul duality patterns in Floer theory (with Yankı Lekili). Uniqueness of area minimizing surfaces for extreme curves (with Baris Coskunuzer), Revista Matematica Iberoamericana 30 () Tight contact structures on laminar free hyperbolic .
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Low-Dimensional and Symplectic Topology (Proceedings of Symposia in Pure Mathematics) by Michael Usher (Author) ISBN ISBN Why is ISBN important.
ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Author: Michael Usher.
Low-dimensional and symplectic topology: Georgia International Topology Conference, May 18–29,University of Georgia, Athens, Georgia / Michael Usher, editor.
— (Proceedings of symposia in pure mathematics ; v. 82) Includes bibliographical references. ISBN (alk. paper) 1. Low-dimensional topology—Congresses. This volume contains the proceedings of the conference, which includes survey and research articles concerning such areas as knot theory, contact and symplectic topology, 3-manifold theory, geometric group theory, and equivariant topology.
I am interested in all areas of low-dimensional Topology. More specifically, I am interested in trisections of smooth 4-manifolds (with and without boundary), generic maps and Lefschetz fibrations on 4-manifolds, symplectic and contact topology, open book decompositions of 3-manifolds, and anything to do with Heegaard splittings of 3-manifolds.
low–dimensional topology. In part, the hope was to foster dialogue across closely related disciplines, some of which were developing in relative isolation until fairly recently. The lectures centered on several topics, including Heegaard Floer theory, knot theory, symplectic and contact topology, and Seiberg–Witten theory.
This. : Geometry of Low-Dimensional Manifolds, Vol. 2: Symplectic Manifolds and Jones-Witten Theory (London Mathematical Society Lecture Note Series) (): Donaldson, S.
K.: BooksFormat: Paperback. At the core of low-dimensional topology has been the classification of knots and links in the 3-sphere and the classification of 3- and 4-dimensional manifolds (see Wikipedia for the definitions of basic topological terms). Beginning with the introduction of hyperbolic geometry into knots and 3-manifolds by W.
Thurston in the late s, geometric tools have become vital to the : Robion C. Kirby. Freedman, M.H. and Luo, Feng. Selected Applications of Geometry to Low-Dimensional Topology Providence, RI: American Mathematical Society, Miscelllaneous. J Matousek. Using the Borsuk-Ulam Theorem.
Springer, $50 A.H A whole book on this classic theorem and its many varied applications in geometry and combinatorics. Although this theory is conjecturally isomorphic to Seiberg–Witten theory, it is more topological and combinatorial in flavor and thus easier to work with in certain contexts.
The interaction between gauge theory, low-dimensional topology, and symplectic geometry has led to a number of striking new developments in these fields.
Since then, both symplectic and contact topology have become very robust fields of study in their own right. The aim of this session will be to highlight techniques and recent results in the areas of low-dimensional symplectic Low-dimensional and symplectic topology book contact topology ranging from applications in knot theory to the theory of planar arrangements and singularities.
book decompositions and contact geometry. Bringing these pieces together we discuss the construction of “symplectic caps” which are a key tool in the application of contact/symplectic geometry to low-dimensional topology.
Introduction Contactgeometryhasbeen akeytoolin manyrecentadvancesin low-dimensional topology. This first volume is essentially devoted to what the first words of the book’s title convey, i.e. topology in a symplectic context. We discern that we have here one of those marvels of modern geometry in the large sense, as it were: the interplay between physics, differential geometry, and.
Everything about Low dimensional topology. I would open something like an introductory Low-dimensional and symplectic topology book mechanics book and they would just lay out the mathematical formulation of things without giving any (or, I guess, not satisfactory) motivation about it.
Ah, so you're going to be writing about symplectic structures, or something of that sort. The main focus of this workshop will be on holomorphic curve techniques in low-dimensional topology and symplectic geometry. The workshop is a part of the FRG: Collaborative Research: Topology and Invariants of Smooth 4-Manifolds.
It is funded by NSF Focused Research Grant DMS This volume is based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds.
This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects interact (for example: topology, differential and algebraic geometry and mathematical physics). by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST).
The lectures of the Summer School in Nantes (June ) and of the CAST Summer School in Budapest (July ) provide a nice panorama of many aspects of the present status of contact and symplectic topology.
In this paper we will survey the various forms of convexity in symplectic geometry, paying particular attention to applications of convexity in low-dimensional topology. View Show abstract. Introduction The topology of contact manifolds and symplectic manifolds have become subjects of fundamental importance in low-dimensional topology.
Symplectic Geometry: A proof of the Arnold conjecture by polyfold techniques, withenko,almost (weak) Arnold conjecture is a lower bound on the number of periodic orbits of any periodic Hamiltonian system in terms of. SYMPLECTIC COBORDISMS AND OPEN BOOK DECOMPOSITIONS DAVID T.
GAY 1. Introduction The topology of contact 3–manifolds and symplectic 4–manifolds have become subjects of fundamental importance in low-dimensional topology. Every 3–manifold has a contact structure, but although there has been signiﬁcant progress towards classifying contact.
Title: Lectures on open book decompositions and contact structures Authors: John B. Etnyre (Submitted on 21 Sep (v1), last revised 2 May (this version, v3))Cited by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Introduction The topology of contact manifolds and symplectic manifolds have become subjects of fundamental importance in low-dimensional topology.
Every manifold has a contact structure, but although there has been significant progress towards classifying contact structures on certain classes of manifolds. This article sketches various ideas in contact geometry that have become useful in low-dimensional topology.
Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle attachments, and (3) briefly discuss Giroux's insights into open book decompositions and Cited by: 7.
These striking interplays between the low dimensional topology and symplectic geometry are the main subject of this book, which is freely based on lecture courses given at the Clay Mathematics Institute Summer School in Budapest, Hungary, in These volumes are based on lecture courses and seminars given at the LMS Durham Symposium on the geometry of low-dimensional manifolds.
This area has been one of intense research recently, with major breakthroughs that have illuminated the way a number of different subjects (topology, differential and algebraic geometry and mathematical physics) interact.
Symplectic 4-manifolds and Lefschetz fibrations [video] In the survery we review the basic features of symplectic 4-manifolds which are relevant in the study of mapping class groups. We list some problems which can be verified using methods coming from symplectic topology and show how theorems of, say, Seiberg-Witten theory can be applied in.
In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional homology is a novel invariant that arises as an infinite-dimensional analogue of finite-dimensional Morse homology.
Andreas Floer introduced the first version of Floer homology, now called Lagrangian Floer homology, in his proof of the Arnold conjecture in symplectic geometry. The UCL Geometry and Topology Group is part of the UCL Mathematics Department.
We have eight faculty members, five postdocs and 14 PhD students. Our research interests include differential geometry and geometric analysis, symplectic geometry, gauge theory, low.
Symplectic camel problem, Graduate Geometry and Topology Seminar, Spring ; A geometer's attempt to study the topology of manifolds: Open book decompositions, Graduate Topology Seminar, Spring ; Introduction to moduli spaces of J-holomorphic curves Part I, Graduate Geometry Topology Seminar, Fall Low Dimensional Geometry and Topology Special Feature.
Mathematics. Equivalence of Heegaard Floer homology and embedded contact homology via open book decompositions. Vincent Colin, a, 1 Paolo We are extremely grateful to MSRI and the organizers of the Symplectic and Contact Geometry and Topology and Homology Theories of Knots and Links Cited by: The main goal of the book is to establish the fundamental theorems of the subject in full and rigorous detail.
It may also serve as an introduction to current work in symplectic topology. The second edition clarifies various arguments, includes some additional results, and updates the. The Arf invariant has higher-order generalizations as do the linking numbers of the components of a link.
Conant et al. use these generalizations to give a nearly complete answer to the problem of classifying the Whitney towers that a link can bound in the 4-ball.A link may not bound disjoint surfaces, and therefore, the authors immerse 2-disks, each of which bounds a component of the link Author: Robion C.
Kirby. of many research areas: low dimensional topology, foliation theory, dynamical systems, symplectic topology, and Floer homology theories. Great progress was recently made in this topic, thanks to Giroux’s description of contact structures in terms of open book decompositions.
In dimension 3. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several open problems.
Recently several connections were established with low dimensional topology, symplectic geometry and theory of. Basic definitions; motivation from physics, geometry, and low-dimensional topology.
(cf McDuff-Salamon, Ch. 1) Basic facts about symplectic manifolds and symplectic linear algebra (M-S Ch. 2, 3, 4) Symplectic group actions (M-S Ch. 5) Symplectomorphisms and fixed points (M-S Ch. 8, 9, 10, 11). Based on a series of lectures for graduate students in topology, this book begins with an overview of the closed case, and then proceeds to explain the essentials of Siefring's intersection theory and how to use it, and gives some sample applications in low-dimensional symplectic and contact topology.
The appendices provide valuable information. Low-dimensional topology and geometry Robion C. Kirby1 Department of Mathematics, University of California, Berkeley, CA A t the core of low-dimensional topology has been the classiﬁca-tion of knots and links in the 3-sphere and the classiﬁcation of 3- and 4-dimensional manifolds (see Wikipedia for the deﬁnitions of basic to Author: Robion C.
Kirby. Selman Akbulut is a Turkish mathematician and a Professor at Michigan State University. His research is in topology and he has specifically worked on handlebody theory, low-dimensional manifolds, symplectic topology and G2 manifolds with success in developing 4-dimensional handlebody techniques, settling conjectures and solving problems.
show moreAuthor: Selman Akbulut. The Joint Los Angeles Topology Seminar: Online Zoom Symplectic geometry as topology of odd sphere bundles Alexander invariants are classical objects in low-dimensional topology stemming from a natural module structure on the homology of the universal abelian cover.
This is the natural setting in which to define. This book presents the topology of smooth 4-manifolds in an intuitive self-contained way, developed over a number of years by Professor Akbulut.
The text is aimed at graduate students and focuses on the teaching and learning of the subject, giving a direct approach to constructions and theorems which are supplemented by exercises to help the reader work through the details not covered in the.
Selman Akbulut is a Turkish mathematician and a Professor at Michigan State University. His research is in topology and he has specifically worked on handlebody theory, low-dimensional manifolds, symplectic topology and G2 manifolds with success in developing 4-dimensional handlebody techniques, settling conjectures and solving : Selman Akbulut.This article sketches various ideas in contact geometry that have become useful in low-dimensional topology.
Specifically we (1) outline the proof of Eliashberg and Thurston's results concerning perturbations of foliatoins into contact structures, (2) discuss Eliashberg and Weinstein's symplectic handle attachments, and (3) briefly discuss Giroux's insights into open book decompositions and.