Volume 14, issue 3 (2014)

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

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

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
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
A geometric interpretation of the homotopy groups of the cobordism category

Marcel Bökstedt and Anne Marie Svane

Algebraic & Geometric Topology 14 (2014) 1649–1676
Abstract

The classifying space of the embedded cobordism category has been identified by Galatius, Tillmann, Madsen and Weiss [Acta. Math. 202 (2009) 195–239] as the infinite loop space of a certain Thom spectrum. This identifies the set of path components with the classical cobordism group. In this paper, we give a geometric interpretation of the higher homotopy groups as certain cobordism groups where all manifolds are now equipped with a set of orthonormal sections in the tangent bundle. We also give a description of the fundamental group as a free group with a set of geometrically intuitive relations.

Keywords
cobordism categories, classifying spaces, Thom spectra, fundamental group, vector fields
Mathematical Subject Classification 2010
Primary: 57R90
Secondary: 55Q05
References
Publication
Received: 20 January 2013
Revised: 13 November 2013
Accepted: 20 November 2013
Published: 29 May 2014
Authors
Marcel Bökstedt
Department of Mathematics
Aarhus University
Ny Munkegade 118
DK-8000 Aarhus C
Denmark
Anne Marie Svane
Department of Mathematics
Aarhus University
Ny Munkegade 118
DK-8000 Aarhus C
Denmark