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 pageEdited 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