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.
Author(s): David T. Gay; Weiwei Wu
Series: Proceedings of Symposia in Pure Mathematics 102
Publisher: American Mathematical Society
Year: 2019
Language: English
Commentary: decrypted from 608A428077A373BB2B6D299ECE9C76AE source file
Pages: 282
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 ?_{∞}-structures associated to Lefschetz fibrations. IV
1. Introduction
2. Main constructions
3. ??₂(ℝ)
4. ??₂(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
