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A
geometric interpretation of the homotopy groups of the
cobordism category
Marcel Bökstedt and Anne Marie Svane |
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Algebraic & Geometric Topology 14 (2014) 1649–1676
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Abstract |
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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
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Mathematical Subject Classification 2010
Primary: 57R90
Secondary: 55Q05
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References |
Publication
Received: 20 January 2013
Revised: 13 November 2013
Accepted: 20 November 2013
Published: 29 May 2014
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Authors |
| Marcel Bökstedt | |
| Department of Mathematics Aarhus University Ny Munkegade 118 DK-8000 Aarhus C Denmark |
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| Anne Marie Svane | |
| Department of Mathematics Aarhus University Ny Munkegade 118 DK-8000 Aarhus C Denmark |
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