Vol. 89, No. 2, 1980

Recent Issues
Vol. 331: 1
Vol. 330: 1  2
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN 1945-5844 (electronic)
ISSN 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
A homology spectral sequence for submersions

Patrick C. Endicott and J. Wolfgang Smith

Vol. 89 (1980), No. 2, 279–299
Abstract

By a submersion we shall understand a C surjection f : X Y between paracompact C manifolds with dimX dimY , subject to the condition that the differential of f have maximal rank at all points. This implies that the fiber fy over any point y Y will be a smooth regularly imbedded submanifold of X. Differentiable fiber bundles constitute a special class of submersions, characterized by the existence of local product structures, and in this particular case all fibers fy are homeomorphic to a standerd fiber F. The central result in the homology theory of fiber bundles asserts the existence of a convergent spectral sequence whose E term is the bigraded group associated to some filtration of H(X;G)1, and for which

E2s,t ≈ Hs(Y;Ht(F ;G ))

in case the bundle is orientable over G. In the present paper this result is generalized to arbitrary submersions. The E2 terms now come to be identified with certain groups Hs,t(f;G) representing a homology functor from the category of submersions to the category of bigraded groups, which reduce of course to Hs(Y ;Ht(F;G)) in the classical case.

Mathematical Subject Classification 2000
Primary: 55T10
Secondary: 57R35
Milestones
Received: 23 August 1978
Published: 1 August 1980
Authors
Patrick C. Endicott
J. Wolfgang Smith
http://en.wikipedia.org/wiki/Wolfgang_Smith