Volume 12, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 20
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Subscriptions
Author Index
To Appear
Contacts
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Topological Hochschild homology and cohomology of $A_\infty$ ring spectra

Vigleik Angeltveit

Geometry & Topology 12 (2008) 987–1032
Abstract

Let A be an A ring spectrum. We use the description from our preprint [math.AT/0612165] of the cyclic bar and cobar construction to give a direct definition of topological Hochschild homology and cohomology of A using the Stasheff associahedra and another family of polyhedra called cyclohedra. This construction builds the maps making up the A structure into THH(A), and allows us to study how THH(A) varies over the moduli space of A structures on A.

As an example, we study how topological Hochschild cohomology of Morava K–theory varies over the moduli space of A structures and show that in the generic case, when a certain matrix describing the noncommutativity of the multiplication is invertible, topological Hochschild cohomology of 2–periodic Morava K–theory is the corresponding Morava E–theory. If the A structure is “more commutative”, topological Hochschild cohomology of Morava K–theory is some extension of Morava E–theory.

Keywords
structured ring spectra, Morava K-theory, associahedra, cyclohedra, topological Hochschild homology
Mathematical Subject Classification 2000
Primary: 55P43
Secondary: 18D50, 55S35
References
Publication
Received: 5 April 2007
Accepted: 8 February 2008
Published: 12 May 2008
Proposed: Bill Dwyer
Seconded: Paul Goerss, Ralph Cohen
Authors
Vigleik Angeltveit
University of Chicago
Department of Mathematics
5734 S University Ave
Chicago IL 60637
USA
http://www.math.uchicago.edu/~vigleik