Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Rational fibrations, minimal models, and fibrings of homogeneous spaces


Author: Stephen Halperin
Journal: Trans. Amer. Math. Soc. 244 (1978), 199-224
MSC: Primary 55F20
MathSciNet review: 0515558
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Sullivan's theory of minimal models is used to study a class of maps called rational fibrations, which contains most Serre fibrations.

It is shown that if the total space has finite rank and the fibre has finite dimensional cohomology, then both fibre and base have finite rank.

This is applied to prove that certain homogeneous spaces cannot be the total space of locally trivial bundles.

In addition two main theorems are proved which exhibit a close relation between the connecting homomorphism of the long exact homotopy sequence, and certain properties of the cohomology of fibre and base.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 55F20

Retrieve articles in all journals with MSC: 55F20


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0515558-4
PII: S 0002-9947(1978)0515558-4
Keywords: Rational fibration, minimal model, connecting homomorphism, spaces of finite rank, homogeneous space
Article copyright: © Copyright 1978 American Mathematical Society