Overview
- Initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions
- Explores many important constructions that exhibit the 2-Segal property
- Offers an entry point for readers new to the field by including an elementary formulation of 2-Segal spaces and numerous examples
Part of the book series: Lecture Notes in Mathematics (LNM, volume 2244)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This monograph initiates a theory of new categorical structures that generalize the simplicial Segal property to higher dimensions. The authors introduce the notion of a d-Segal space, which is a simplicial space satisfying locality conditions related to triangulations of d-dimensional cyclic polytopes. Focus here is on the 2-dimensional case. Many important constructions are shown to exhibit the 2-Segal property, including Waldhausen’s S-construction, Hecke-Waldhausen constructions, and configuration spaces of flags. The relevance of 2-Segal spaces in the study of Hall and Hecke algebras is discussed.
Higher Segal Spaces marks the beginning of a program to systematically study d-Segal spaces in all dimensions d. The elementary formulation of 2-Segal spaces in the opening chapters is accessible to readers with a basic background in homotopy theory. A chapter on Bousfield localizations provides a transition to the general theory, formulated interms of combinatorial model categories, that features in the main part of the book. Numerous examples throughout assist readers entering this exciting field to move toward active research; established researchers in the area will appreciate this work as a reference.
Authors and Affiliations
About the authors
Tobias Dyckerhoff is Lichtenberg Professor of Mathematics at the University of Hamburg, Germany. His research interests are centered on higher structures in algebra and geometry, and extend to mathematical physics.
Mikhail Kapranov is Professor of Mathematics at the Kavli Institute for the Physics and Mathematics of the Universe in Japan. His research spans algebra, algebraic geometry and category theory, with a particular interest in using category theory to extend ideas at the interface of algebra and geometry. His previous books include Discriminants, Resultants, and Multidimensional Determinants, with I. M. Gelfand and A. V. Zelevinsky, a Modern Birkhäuser Classic.
Bibliographic Information
Book Title: Higher Segal Spaces
Authors: Tobias Dyckerhoff, Mikhail Kapranov
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-27124-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-27122-0Published: 18 October 2019
eBook ISBN: 978-3-030-27124-4Published: 17 October 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XV, 218
Number of Illustrations: 137 b/w illustrations, 2 illustrations in colour
Topics: Category Theory, Homological Algebra, K-Theory, Algebraic Topology