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2018 The $A_\infty$-structure of the index map
Oliver Bräunling, Michael Groechenig, Jesse Wolfson
Ann. K-Theory 3(4): 581-614 (2018). DOI: 10.2140/akt.2018.3.581

Abstract

Let F be a local field with residue field k. The classifying space of GLn(F) comes canonically equipped with a map to the delooping of the K-theory space of k. Passing to loop spaces, such a map abstractly encodes a homotopy coherently associative map of A-spaces GLn(F)Kk. Using a generalized Waldhausen construction, we construct an explicit model built for the A-structure of this map, built from nested systems of lattices in Fn. More generally, we construct this model in the framework of Tate objects in exact categories, with finite dimensional vector spaces over local fields as a motivating example.

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Oliver Bräunling. Michael Groechenig. Jesse Wolfson. "The $A_\infty$-structure of the index map." Ann. K-Theory 3 (4) 581 - 614, 2018. https://doi.org/10.2140/akt.2018.3.581

Information

Received: 24 May 2016; Revised: 7 June 2018; Accepted: 21 June 2018; Published: 2018
First available in Project Euclid: 5 January 2019

zbMATH: 07000853
MathSciNet: MR3892960
Digital Object Identifier: 10.2140/akt.2018.3.581

Subjects:
Primary: 19D55
Secondary: 19K56

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.3 • No. 4 • 2018
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