Vol. 41, No. 3, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
Twisted cohomology theories and the single obstruction to lifting

Lawrence Louis Larmore

Vol. 41 (1972), No. 3, 755–769

Consider any fibration p : E B, any finite C. W.—pair (K,L), and any maps f : K B and h : L E such that p h = f|L. A map g : K E such that p g = f and g|L = h we call a lifting of frelh.

In this paper single obstruction Γ(f) H(K,L,f;g) is defined. g is a so-called B-spectrum, and H ( ; g) is cohomology in that spectrum. If a lifting of f rel h exists, Γ(f) = 0; this condition is also sufficient if the fiber of p is k-connected and dim(K∕L) 2k + 1.

If g0 and g1 are liftings of f rel h, a single obstruction δ(g0,g1;h) H(K,L,f : g) is also defined; if g0 and g1 are connected by a homotopy of liftings of f rel (g0,g1;h) = 0; this condition is, also sufficient if p is k-connected and dim(K∕L) 2k.

In §4, a spectral sequence is constructed for cohomology in a B-spectrum, based on the Postnikov tower of that spectrum, and the relationship between the single obstruction and the classical obstructions is defined.

Mathematical Subject Classification
Primary: 55G35
Received: 23 June 1970
Revised: 8 April 1971
Published: 1 June 1972
Lawrence Louis Larmore