Volume 12, issue 2 (2012)

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

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
Other MSP Journals
An equivariant generalization of the Miller splitting theorem

Harry E Ullman

Algebraic & Geometric Topology 12 (2012) 643–684

Let G be a compact Lie group. We build a tower of G–spectra over the suspension spectrum of the space of linear isometries from one G–representation to another. The stable cofibres of the maps running down the tower are certain interesting Thom spaces. We conjecture that this tower provides an equivariant extension of Miller’s stable splitting of Stiefel manifolds. We provide a cohomological obstruction to the tower producing a splitting in most cases; however, this obstruction does not rule out a split tower in the case where the Miller splitting is possible. We claim that in this case we have a split tower which would then produce an equivariant version of the Miller splitting and prove this claim in certain special cases, though the general case remains a conjecture. To achieve these results we construct a variation of the functional calculus with useful homotopy-theoretic properties and explore the geometric links between certain equivariant Gysin maps and residue theory.

isometry, Miller splitting, cofibre sequence, functional calculus, Gysin map, residue
Mathematical Subject Classification 2010
Primary: 55P42, 55P91, 55P92
Received: 31 March 2011
Revised: 28 November 2011
Accepted: 20 December 2011
Published: 8 April 2012
Harry E Ullman
School of Mathematics and Statistics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
RSMB Television Research Ltd
The Communications Building
48 Leicester Square
London WC2H 7LT