Categorification in geometry, topology, and physics

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 va...

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Bibliographic Details
Main Authors: Beliakova, Anna, Lauda, Aaron D.
Format: eBook Book
Language:English
Published: Providence, R.I American Mathematical Society 2017
Edition:1
Series:Contemporary mathematics
Subjects:
Categories (Mathematics)
Geometry
Mathematical analysis
Physics
Topology
ISBN:1470428210, 9781470428211
Online Access:Get full text
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Summary: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.
Bibliography:Includes bibliographical references
ISBN:1470428210
9781470428211
DOI:10.1090/conm/284