Categorification in geometry, topology, and physics
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Bibliographic Information
Categorification in geometry, topology, and physics
（Contemporary mathematics, 684）
American Mathematical Society, c2017
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Categorification
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Includes bibliographical references
Description and Table of Contents
Description
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.
Table of Contents
B. Webster, Geometry and categorification
Y. Li, A geometric realization of modified quantum algebras
T. Lawson, R. Lipshitz, and S. Sarkar, The cube and the Burnside category
S. Chun, S. Gukov, and D. Roggenkamp, Junctions of surface operators and categorification of quantum groups
R. Rouquier, Khovanov-Rozansky homology and 2-braid groups
I. Cherednik and I. Danilenko, DAHA approach to iterated torus links.
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