Advanced Courses in Mathematics - CRM Barcelona

Building Bridges Between Algebra and Topology

Authors: Chachólski, W., Dyckerhoff, T., Greenlees, J., Stevenson, G.

Editors: Herbera, Dolors, Pitsch, Wolfgang, Zarzuela, Santiago (Eds.)

  • Offers a unique combination of exciting new topics in the crossroad between commutative algebra, representation theory and homotopy theory
  • Provides a great introduction to higher hall algebras
  • Presents a self-contained introduction, with illustrative examples, to the translation of classical commutative algebra concepts to homotopy theory
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eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-319-70157-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA in USD
  • ISBN 978-3-319-70156-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

This volume presents an elaborated version of lecture notes for two advanced courses: (Re)Emerging methods in Commutative Algebra and Representation Theory and Building Bridges Between Algebra and Topology, held at the CRM in the spring of 2015.

Homological algebra is a rich and ubiquitous area; it is both an active field of research and a widespread toolbox for many mathematicians. Together, these notes introduce recent applications and interactions of homological methods in commutative algebra, representation theory and topology, narrowing the gap between specialists from different areas wishing to acquaint themselves with a rapidly growing field. The covered topics range from a fresh introduction to the growing area of support theory for triangulated categories to the striking consequences of the formulation in the homotopy theory of classical concepts in commutative algebra. Moreover, they also include a higher categories view of Hall algebras and an introduction to the use of idempotent functors in algebra and topology.

 

About the authors

Tobias Dyckerhoff is a Junior Fellow at the Hausdorff Center for Mathematics in Bonn, Germany.

Greg Stevenson is a Research Assistant at the Bielefeld University in Germany.

John Greenlees is a Professor at the The University of Sheffield in the United Kingdom.

Wojciech Chachólski is a Professor at the KTH Royal Institute of Technology in Stockholm, Sweden.

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Table of contents (4 chapters)

  • Higher Categorical Aspects of Hall Algebras

    Dyckerhoff, Tobias

    Pages 1-61

  • A Tour of Support Theory for Triangulated Categories Through Tensor Triangular Geometry

    Stevenson, Greg

    Pages 63-101

  • Homotopy Invariant Commutative Algebra over Fields

    Greenlees, John

    Pages 103-169

  • Idempotent Symmetries in Algebra and Topology

    Chachólski, Wojciech

    Pages 171-224

Buy this book

eBook $29.99
price for USA in USD (gross)
  • ISBN 978-3-319-70157-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $39.99
price for USA in USD
  • ISBN 978-3-319-70156-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Building Bridges Between Algebra and Topology
Authors
Editors
  • Dolors Herbera
  • Wolfgang Pitsch
  • Santiago Zarzuela
Series Title
Advanced Courses in Mathematics - CRM Barcelona
Copyright
2018
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-70157-8
DOI
10.1007/978-3-319-70157-8
Softcover ISBN
978-3-319-70156-1
Series ISSN
2297-0304
Edition Number
1
Number of Pages
XIII, 225
Topics