Building Bridges Between Algebra and Topology

Wojciech Chachólski, Tobias Dyckerhoff, John Greenlees , Greg Stevenson

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English

Birkhauser Verlag AG
13 April 2018

Mathematical foundations; Algebra; Algebraic topology

Series: Advanced Courses in Mathematics - CRM Barcelona

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.

By: Wojciech Chachólski, Tobias Dyckerhoff, John Greenlees, Greg Stevenson
Edited by: Dolors Herbera
Imprint: Birkhauser Verlag AG
Country of Publication: Switzerland
Edition: 2018 ed.
Dimensions: Height: 240mm, Width: 168mm,
Weight: 454g
ISBN: 9783319701561
ISBN 10: 3319701568
Series: Advanced Courses in Mathematics - CRM Barcelona
Pages: 225
Publication Date: 13 April 2018
Audience: College/higher education , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Higher Categorical Aspects of Hall Algebras.- Support Theory for Triangulated Categories.- Homotopy Invariant Commutative Algebra over Fields.- Idempotent Symmetries in Algebra and Topology.

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.