Vol. 3, No. 4, 2018

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 2379-1691 (e-only)
ISSN: 2379-1683 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
The $A_\infty$-structure of the index map

Oliver Braunling, Michael Groechenig and Jesse Wolfson

Vol. 3 (2018), No. 4, 581–614

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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Waldhausen construction, boundary map in $K“$-theory, Tate space
Mathematical Subject Classification 2010
Primary: 19D55
Secondary: 19K56
Received: 24 May 2016
Revised: 7 June 2018
Accepted: 21 June 2018
Published: 18 December 2018
Oliver Braunling
Freiburg Institute for Advanced Studies
University of Freiburg
Mathematical Institute
University of Bonn
Michael Groechenig
Department of Mathematics
University of Toronto
Toronto, ON
Jesse Wolfson
Department of Mathematics
University of California
Irvine, CA
United States