Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 14, Number 1 (2014), 299-347.
On the map of Bökstedt–Madsen from the cobordism category to $A$–theory
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 .
Algebr. Geom. Topol., Volume 14, Number 1 (2014), 299-347.
Received: 14 October 2011
Revised: 22 June 2013
Accepted: 22 June 2013
First available in Project Euclid: 19 December 2017
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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