**Contemporary Mathematics**

Volume: 613;
2014;
176 pp;
Softcover

MSC: Primary 57; 81; 18; 55;

Print ISBN: 978-1-4704-1015-5

Product Code: CONM/613

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

**Electronic ISBN: 978-1-4704-1552-5
Product Code: CONM/613.E**

List Price: $78.00

AMS Member Price: $62.40

MAA member Price: $70.20

# Topology and Field Theories

Share this page *Edited by *
*Stephan Stolz*

This book is a collection of expository articles based on four lecture
series presented during the 2012 Notre Dame Summer School in Topology
and Field Theories.

The four topics covered in this volume are: Construction of a local
conformal field theory associated to a compact Lie group, a level and
a Frobenius object in the corresponding fusion category; Field theory
interpretation of certain polynomial invariants associated to knots
and links; Homotopy theoretic construction of far-reaching
generalizations of the topological field theories that Dijkgraf and
Witten associated to finite groups; and a discussion of the action of
the orthogonal group \(O(n)\) on the full subcategory of an
\(n\)-category consisting of the fully dualizable objects.

The expository style of the articles enables non-experts to
understand the basic ideas of this wide range of important
topics.

#### Readership

Graduate students and research mathematicians interested in field theories from an algebraic topology and higher category perspective.

# Table of Contents

## Topology and Field Theories

- Preface v6 free
- Three-Tier CFTs from Frobenius Algebras 110 free
- Lectures on Knot Homology and Quantum Curves 4150
- Ambidexterity 7988
- Dualizability in Low-Dimensional Higher Category Theory 111120
- Introduction 111120
- Higher categories 113122
- 1. Strict n-Categories 114123
- 2. Bicategories 115124
- 3. Higher Categories: Hypotheses of Baez and Dolan 119128
- 4. Segal Categories 122131
- 5. Higher Categories: Segal n-categories 125134
- 6. Dualizability in 2-categories 128137
- 7. Duality in Higher Categories 130139
- 8. The Cobordism Hypothesis 132141
- 9. Exercises 134143
- Understanding the 𝑂(1)-action 135144
- 10. Defining categories via generators and relations 135144
- 11. Presentations for low-dimensional bordism categories 136145
- 12. The 𝑂(1)-action via Presentations 137146
- 13. Unoriented Bordism as a Homotopy Orbit 138147
- 14. Exercises 140149
- Understanding the 𝑂(2)-action 141150
- 15. The Serre automorphism 141150
- 16. 2-full dualizability and the action of 𝑂(2) 143152
- 17. Reducing to the study of simply connected 3-types 144153
- 18. Applying Whitehead’s construction to higher categories 147156
- 19. Exercises 150159
- Understanding the 𝑂(3)-action 150159
- 20. 3-full dualizability and the action of 𝑂(3) 150159
- 21. The data of an 𝑆𝑂(3) action 154163
- 22. An application to fusion categories 155164
- 23. Exercises 156165
- The Unicity Theorem 156165
- 24. Introduction to the Unicity Theorem 156165
- 25. Homotopy theories 157166
- 26. (∞,1)-categories 159168
- 27. The Unicity Theorem 164173
- Acknowledgements 173182
- References 173182