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⁺¹ →^∂_n ΩF_n → 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