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

Filtering the fiber of the pinch map

Brayton Gray

Geometry & Topology Monographs 13 (2008) 203–227

DOI: 10.2140/gtm.2008.13.203

arXiv: 0804.1896

Abstract

A new type of Hopf invariant is described for the fiber of the pinch map:
F → X ∪CA →π SA
and this is used to study the boundary map in the fibration sequence of Cohen, Moore and Neisendorfer:
Ω2S2n+1n ΩFn → ΩP2n+1 → ΩS2n+1.
The boundary map is shown to be compatible with the Hopf invariant and a filtration of the spliting is obtained.

Keywords

Moore space, Hopf invariant

Mathematical Subject Classification

Primary: 55P99, 55Q20

Secondary: 55Q25

References
Publication

Received: 24 July 2006
Revised: 19 January 2007
Accepted: 26 January 2007
Published: 22 2008

Authors
Brayton Gray
Dept of Math, Stats and Comp Sci (M/C 249)
University of Illinois at Chicago
851 South Morgan Street
Chicago, IL 60607-7045
USA