Annals of K-Theory
- Ann. K-Theory
- Volume 3, Number 4 (2018), 581-614.
The $A_\infty$-structure of the index map
Let be a local field with residue field . The classifying space of comes canonically equipped with a map to the delooping of the -theory space of . Passing to loop spaces, such a map abstractly encodes a homotopy coherently associative map of -spaces . Using a generalized Waldhausen construction, we construct an explicit model built for the -structure of this map, built from nested systems of lattices in . 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.
Ann. K-Theory, Volume 3, Number 4 (2018), 581-614.
Received: 24 May 2016
Revised: 7 June 2018
Accepted: 21 June 2018
First available in Project Euclid: 5 January 2019
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Bräunling, Oliver; Groechenig, Michael; Wolfson, Jesse. The $A_\infty$-structure of the index map. Ann. K-Theory 3 (2018), no. 4, 581--614. doi:10.2140/akt.2018.3.581. https://projecteuclid.org/euclid.akt/1546657257