گستردگی در توپولوژی معاصر: کنفرانس بین‌المللی توپولوژی جورجیا ۲۰۱۷، ۲۲ مه - ۲ ژوئن ۲۰۱۷، دانشگاه جورجیا، آتن، جورجیا

This volume contains the proceedings of the 2017 Georgia International Topology Conference, held from May 22 June 2, 2017, at the University of Georgia, Athens, Georgia. The papers contained in this volume cover topics ranging from symplectic topology to classical knot theory to topology of 3- and 4-dimensional manifolds to geometric group theory. Several papers focus on open problems, while other papers present new and insightful proofs of classical results. Taken as a whole, this volume captures the spirit of the conference, both in terms of public lectures and informal conversations, and presents a sampling of some of the great new ideas generated in topology over the preceding eight years. Cover Title page Contents Preface Structure of the flow and Yamada polynomials of cubic graphs 1. Introduction 2. Graph polynomials, algebras and categories 3. The golden identity for the Yamada polynomial 4. Structure of the flow polynomial (mod 5) 5. Golden inequality for non-planar cubic graphs 6. Exponential growth of the number of chromatic polynomials 7. Appendix: A proof of the golden identity for planar cubic graphs Acknowledgments References Inequivalent Lefschetz fibrations on rational and ruled surfaces 1. Introduction 2. Preliminaries 3. Constructions Acknowledgments References Virtual and welded periods of classical knots 1. Periodic virtual knots and Wirtinger presentations 2. The group of outer automorphisms 3. Automorphisms of knot groups 4. Lifting periodic homeomorphisms 5. Proof of Theorem 3 Acknowledgments References Transverse universal links 1. Introduction 2. Background 3. Transverse universal links Acknowledgments References Groups and polytopes 1. Introduction 2. Definition of the polytope invariant of groups 3. Examples 4. Marked polytopes 5. The polytope invariant and intrinsic properties of the group 6. Questions Acknowledgments References Functions on surfaces and constructions of manifolds in dimensions three, four and five 1. Introduction 2. Generic families of functions 3. The main theorem 4. Handlebodies from single functions and Heegaard splittings 5. 1-parameter families and 4-manifolds 6. 2-parameter families and 5-manifolds References On braided, banded surfaces and ribbon obstructions 1. Introduction 2. Obtaining ribbon obstructions from braid conjugacy class invariants 3. The annular Rasmussen invariant does not give new ribbon obstructions Acknowledgments References A remark on the geography problem in Heegaard Floer homology 1. Introduction 2. Background 3. Proof of Theorem 1 4. Proof of Corollary 3 References A note on knot concordance and involutive knot Floer homology 1. Introduction 2. Background 3. Proof of Theorem Acknowledgments References A Heegaard Floer analog of algebraic torsion 1. Introduction 2. The ech chain complex 3. Hutchings’s filtration in ech 4. Porting Hutchings’s filtration to Heegaard Floer homology Acknowledgments References Realization problems for diffeomorphism groups 1. Introduction 2. Cohomological techniques 3. Dynamical obstructions to realizations 4. Positive results Acknowledgments References Problems, questions, and conjectures about mapping class groups 1. Linearity 2. The congruence subgroup problem 3. The integral Burau representation 4. Generating with torsion 5. Generators and relations for Torelli groups 6. Virtual surjection onto the integers 7. Ivanov’s metaconjecture 8. Normal right-angled Artin subgroups 9. Cohomology of the mapping class group 10. Pseudo-Anosov theory Acknowledgments References Totally disconnected groups (not) acting on two-manifolds Acknowledgment References Fukaya A_{∞}-structures associated to Lefschetz fibrations. IV 1. Introduction 2. Main constructions 3. sl2(R) 4. sl2(R)-connections on surfaces 5. TQFT considerations 6. The differentiation axiom 7. Elliptic holonomy 8. Maps to the disc 9. Floer cohomology 10. Conclusion Acknowledgments References 2017 GITC Problem Sessions References Back Cover