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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Pullback de Rham cohomology of the free path fibration


Author: Kuo-Tsai Chen
Journal: Trans. Amer. Math. Soc. 242 (1978), 307-318
MSC: Primary 58A10; Secondary 55D99, 58A99
Erratum: Trans. Amer. Math. Soc. 250 (1979), 398-398.
MathSciNet review: 0478190
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Abstract: Let M and N be smooth manifolds and let $ \bar B (A)$ be the reduced bar construction on the de Rham complex $ \Lambda (M)$ or a suitable subcomplex A of M. For every smooth map $ f:N \to M \times M$, the tensor product $ \Lambda (N) \otimes \bar B(A)$, equipped with a suitable differential, will yield the correct cohomology for the pullback of the free path fibration $ P(M) \to M \times M$ via the smooth map F. Moreover, $ \Lambda (N) \otimes \bar B(A)$ can be taken as a de Rham subcomplex of the pullback space.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0478190-7
PII: S 0002-9947(1978)0478190-7
Keywords: Differential forms, path spaces, fibration, two sided bar construction, Eilenberg-Moore spectral sequence
Article copyright: © Copyright 1978 American Mathematical Society