**Contemporary Mathematics**

Volume: 684;
2017;
267 pp;
Softcover

MSC: Primary 81; 57; 14; 18; 58; 17; 20;

**Print ISBN: 978-1-4704-2821-1
Product Code: CONM/684**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

**Electronic ISBN: 978-1-4704-3691-9
Product Code: CONM/684.E**

List Price: $111.00

AMS Member Price: $88.80

MAA Member Price: $99.90

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# Categorification in Geometry, Topology, and Physics

Share this page *Edited by *
*Anna Beliakova; Aaron D. Lauda*

The emergent mathematical philosophy of
categorification is reshaping our view of modern mathematics by
uncovering a hidden layer of structure in mathematics, revealing
richer and more robust structures capable of describing more complex
phenomena. Categorification is a powerful tool for relating various
branches of mathematics and exploiting the commonalities between
fields. It provides a language emphasizing essential features and
allowing precise relationships between vastly different fields.

This volume focuses on the role categorification plays in geometry,
topology, and physics. These articles illustrate many important trends
for the field including geometric representation theory, homotopical
methods in link homology, interactions between higher representation
theory and gauge theory, and double affine Hecke algebra approaches to
link homology.

The companion volume (Contemporary Mathematics, Volume 683) is
devoted to categorification and higher representation theory.

#### Readership

Graduate students and research mathematicians interested in categorification, link homology, and geometric representation theory.

# Table of Contents

## Categorification in Geometry, Topology, and Physics

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Geometry and categorification 112
- A geometric realization of modified quantum algebras 2334
- The cube and the Burnside category 6374
- Junctions of surface operators and categorification of quantum groups 8798
- 1. Introduction 8899
- 2. Junctions of Wilson lines and quantum groups 91102
- 3. Junctions of surface operators 105116
- 3.1. Junctions in 4d \CN=4 theory 110121
- 3.2. Line-changing operators in class \CS and network cobordisms 111122
- 3.3. Junctions in 4d \CN=2 theory 112123
- 3.4. Junctions in 4d \CN=1 theory 113124
- 3.5. OPE of surface operators and the Horn problem 113124
- 3.6. OPE and Schubert calculus 117128
- Domain walls in 4d \CN=2 SQCD 120131

- 4. Categorification and the Landau-Ginzburg perspective 120131
- 5. What’s next? 134145
- Acknowledgments 135146
- Appendix A. Wilson lines and categories 𝑁Web 135146
- Appendix B. Domain walls, junctions and Grassmannians 137148
- Appendix C. LG Interfaces and the cohomology of Grassmannians 138149
- Appendix D. LG Interfaces and 2-categories 𝑁Foam 138149
- References 142153

- Khovanov-Rozansky homology and 2-braid groups 147158
- DAHA approach to iterated torus links 159170
- 0. Introduction 161172
- 1. Double Hecke algebras 170181
- 2. Integral forms 177188
- 3. Topological vertex 185196
- 4. DAHA-Jones theory 195206
- 5. DAHA-superpolynomials 209220
- 6. Multiple torus knots 219230
- 7. Hopf links 228239
- 8. Further examples 238249
- 9. Generalized twisted union 246257
- Appendix A. Links and splice diagrams 255266
- References 265276

- Back Cover Back Cover1282