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Abstract
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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.
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Keywords
cobordism category, mapping class group, homological
stability, infinite loop space
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Mathematical Subject Classification 2000
Primary: 55P47, 57M99, 57R50
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Publication
Received: 2 July 2008
Revised: 29 November 2008
Accepted: 19 December 2008
Published: 28 April 2009
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