Volume 13 (2008)

Download this article
For screen
For printing
Recent Volumes
Volume 1, 1998
Volume 2, 1999
Volume 3, 2000
Volume 4, 2002
Volume 5, 2002
Volume 6, 2003
Volume 7, 2004
Volume 8, 2006
Volume 9, 2006
Volume 10, 2007
Volume 11, 2007
Volume 12, 2007
Volume 13, 2008
Volume 14, 2008
Volume 15, 2008
Volume 16, 2009
Volume 17, 2011
Volume 18, 2012
Volume 19, 2015
The Series
MSP Books and Monographs
About this Series
Editorial Board
Ethics Statement
Author Index
Submission Guidelines
Author Copyright Form
Purchases
ISSN (electronic): 1464-8997
ISSN (print): 1464-8989
Other MSP Publications

Computation of the homotopy of the spectrum tmf

Tilman Bauer

Geometry & Topology Monographs 13 (2008) 11–40

DOI: 10.2140/gtm.2008.13.11

arXiv: math/0311328

Abstract

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in each of the latter two cases, a sequence of algebraic Bockstein spectral sequences is used to compute the E2 term of the elliptic Adams–Novikov spectral sequence from the elliptic curve Hopf algebroid. In a further step, all the differentials in the latter spectral sequence are determined. The result of this computation is originally due to Hopkins and Mahowald (unpublished).

Keywords

topological modular forms, elliptic cohomology, Adams–Novikov spectral sequence

Mathematical Subject Classification

Primary: 55N34

Secondary: 55T15

References
Publication

Received: 30 September 2005
Revised: 1 September 2006
Accepted: 11 October 2006
Published: 22 February 2008

Authors
Tilman Bauer
Mathematisches Institut der Universität Münster
Einsteinstr. 62
48149 Münster
Germany
http://wwwmath.uni-muenster.de/u/tbauer/