Lecture Notes in Mathematics

Higher Segal Spaces

Authors: Dyckerhoff, Tobias, Kapranov, Mikhail

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  • 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
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  • ISBN 978-3-030-27124-4
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Softcover $49.99
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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 in terms 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.

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.

Table of contents (11 chapters)

Table of contents (11 chapters)

Buy this book

eBook $39.99
price for USA in USD (gross)
  • ISBN 978-3-030-27124-4
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $49.99
price for USA in USD
  • ISBN 978-3-030-27122-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Higher Segal Spaces
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2244
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-27124-4
DOI
10.1007/978-3-030-27124-4
Softcover ISBN
978-3-030-27122-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XV, 218
Number of Illustrations
137 b/w illustrations, 2 illustrations in colour
Topics