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The Homotopy Type of Fredholm Manifolds

Kalyan K. Mukherjea
Transactions of the American Mathematical Society
Vol. 149, No. 2 (Jun., 1970), pp. 653-663
DOI: 10.2307/1995419
Stable URL: http://www.jstor.org/stable/1995419
Page Count: 11
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The Homotopy Type of Fredholm Manifolds
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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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