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An open-closed cobordism category with background space

Elizabeth Hanbury
Algebraic & Geometric Topology 9 (2009) 833–863
DOI: 10.2140/agt.2009.9.833
Abstract

In this paper we introduce an open-closed cobordism category with maps to a background space. We identify the classifying space of this category for certain classes of background space. The key ingredient is the homology stability of mapping class groups with twisted coefficients.

Keywords
cobordism category, mapping class group, homological stability, infinite loop space
Mathematical Subject Classification 2000
Primary: 55P47, 57M99, 57R50
References
Publication
Received: 2 July 2008
Revised: 29 November 2008
Accepted: 19 December 2008
Published: 28 April 2009
Authors
Elizabeth Hanbury
Department of Mathematics
University of Durham
Science Laboratories, South Road
Durham DH1 3LE
UK