Algebraic & Geometric Topology

On the map of Bökstedt–Madsen from the cobordism category to $A$–theory

George Raptis and Wolfgang Steimle

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Abstract

Bökstedt and Madsen defined an infinite loop map from the embedded d–dimensional cobordism category of Galatius, Madsen, Tillmann and Weiss to the algebraic K–theory of BO(d) 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 A–theory Euler characteristic of smooth bundles with compact d–dimensional fibers, as defined by Dwyer, Weiss and Williams. The second result is that it actually factors through the canonical unit map Q(BO(d)+)A(BO(d)).

Article information

Source
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 299-347.

Dates
Received: 14 October 2011
Revised: 22 June 2013
Accepted: 22 June 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715802

Digital Object Identifier
doi:10.2140/agt.2014.14.299

Mathematical Reviews number (MathSciNet)
MR3158761

Zentralblatt MATH identifier
1299.19001

Subjects
Primary: 19D10: Algebraic $K$-theory of spaces 55R12: Transfer 57R90: Other types of cobordism [See also 55N22]

Keywords
cobordism category bivariant $A$–theory parametrized Euler characteristic

Citation

Raptis, George; Steimle, Wolfgang. On the map of Bökstedt–Madsen from the cobordism category to $A$–theory. Algebr. Geom. Topol. 14 (2014), no. 1, 299--347. doi:10.2140/agt.2014.14.299. https://projecteuclid.org/euclid.agt/1513715802


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