Download this article
 Download this article For screen
For printing
Recent Issues

Volume 24
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Oriented and unitary equivariant bordism of surfaces

Andrés Ángel, Eric Samperton, Carlos Segovia and Bernardo Uribe

Algebraic & Geometric Topology 24 (2024) 1623–1654
Abstract

Fix a finite group G. We study Ω2SO ,G and Ω2U,G, the unitary and oriented bordism groups of smooth G–equivariant compact surfaces, respectively, and we calculate them explicitly. Their ranks are determined by the possible representations around fixed points, while their torsion subgroups are isomorphic to the direct sum of the Bogomolov multipliers of the Weyl groups of representatives of conjugacy classes of all subgroups of G. We present an alternative proof of the fact that surfaces with free actions which induce nontrivial elements in the Bogomolov multiplier of the group cannot equivariantly bound. This result permits us to show that the 2–dimensional SK –groups (Schneiden und Kleben, or “cut and paste”) of the classifying spaces of a finite group can be understood in terms of the bordism group of free equivariant surfaces modulo the ones that bound arbitrary actions.

Keywords
equivariant bordism, equivariant vector bundle, surface
Mathematical Subject Classification
Primary: 55N22, 57R75, 57R77, 57R85
References
Publication
Received: 30 April 2022
Revised: 13 February 2023
Accepted: 26 February 2023
Published: 28 June 2024
Authors
Andrés Ángel
Departamento de Matemáticas
Universidad de los Andes
Bogota
Colombia
Eric Samperton
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL
United States
Mathematics Department
Purdue University
West Lafayette, IN
United States
Carlos Segovia
Instituto de Matemáticas
UNAM Unidad Oaxaca
Oaxaca
Mexico
Bernardo Uribe
Max Planck Institut für Mathematik
Bonn
Germany
Departamento de Matemáticas y Estadística
Universidad del Norte
Barranquilla
Colombia
https://sites.google.com/site/bernardouribejongbloed/

Open Access made possible by participating institutions via Subscribe to Open.