Breadth in contemporary topology : 2017 Georgia International Topology Conference, May 22-June 2, 2017, University of Georgia, Athens, Georgia / David T. Gay, Weiwei Wu, editors.

Format:

Book

Author/Creator:

Gay, David T., 1968- editor.

Contributor:

Wu, Weiwei, 1983- editor.

Series:

Proceedings of symposia in pure mathematics ; Volume 102.

Proceedings of symposia in pure mathematics ; Volume 102

Language:

English

Subjects (All):

Topology--Congresses.

Topology.

Homology theory--Congresses.

Homology theory.

Manifolds (Mathematics)--Congresses.

Manifolds (Mathematics).

Physical Description:

1 online resource (298 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2019]

Language Note:

English

Summary:

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.

Contents:

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

2. Preliminaries

3. Constructions

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

Transverse universal links

2. Background

3. Transverse universal links

Groups and polytopes

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

Functions on surfaces and constructions of manifolds in dimensions three, four and five

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

On braided, banded surfaces and ribbon obstructions

2. Obtaining ribbon obstructions from braid conjugacy class invariants

3. The annular Rasmussen invariant does not give new ribbon obstructions.

Acknowledgments

A remark on the geography problem in Heegaard Floer homology

3. Proof of Theorem 1

4. Proof of Corollary 3

A note on knot concordance and involutive knot Floer homology

3. Proof of Theorem

A Heegaard Floer analog of algebraic torsion

2. The ech chain complex

3. Hutchings's filtration in ech

4. Porting Hutchings's filtration to Heegaard Floer homology

Realization problems for diffeomorphism groups

2. Cohomological techniques

3. Dynamical obstructions to realizations

4. Positive results

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

Totally disconnected groups (not) acting on two-manifolds

Acknowledgment

Fukaya _{∞}-structures associated to Lefschetz fibrations. IV

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

2017 GITC Problem Sessions

Back Cover.

Notes:

Includes bibliographical references.

Description based on print version record.

Description based on publisher supplied metadata and other sources.

ISBN:

9781470452599

1470452596

OCLC:

1108535894