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

 

The homotopy type of Fredholm manifolds


Author: Kalyan K. Mukherjea
Journal: Trans. Amer. Math. Soc. 149 (1970), 653-663
MSC: Primary 57.55
MathSciNet review: 0259954
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Abstract: Banach manifolds whose tangent bundles admit a reduction to the Fredholm group have been intensively studied in the last few years. Here we show that such a manifold (under appropriate smoothness and separability restrictions) is homotopy equivalent to the union of a nested sequence of closed finite-dimensional submanifolds.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1970-0259954-4
PII: S 0002-9947(1970)0259954-4
Keywords: Fredholm manifold, filtration, homotopy type, orientation
Article copyright: © Copyright 1970 American Mathematical Society