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On the map of
Bökstedt–Madsen from the cobordism category to
$A\!$–theory
George Raptis and Wolfgang Steimle |
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Algebraic & Geometric Topology 14 (2014) 299–347
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Abstract |
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Bökstedt and Madsen defined an infinite loop map from the embedded –dimensional cobordism category of Galatius, Madsen, Tillmann and Weiss to the algebraic –theory of in the sense of Waldhausen. The purpose of this paper is to establish two results in relation to this map. The first result is that it extends the universal parametrized –theory Euler characteristic of smooth bundles with compact –dimensional fibers, as defined by Dwyer, Weiss and Williams. The second result is that it actually factors through the canonical unit map . |
Keywords
cobordism category, bivariant $A$–theory, parametrized
Euler characteristic
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Mathematical Subject Classification 2010
Primary: 19D10, 55R12, 57R90
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References |
Publication
Received: 14 October 2011
Revised: 22 June 2013
Accepted: 22 June 2013
Preview posted: 5 December 2014
Published: 9 January 2014
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Authors |
| George Raptis | |
| Institut für Mathematik Universität Osnabrück Albrechtstr. 28a D-49076 Osnabrück Germany |
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| Wolfgang Steimle | |
| Institut for Matematiske Fag University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Ø Denmark |
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