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2001 The tangent bundle of an almost-complex free loopspace
Jack Morava
Homology Homotopy Appl. 3(2): 407-415 (2001).

Abstract

The space $LV$ of free loops on a manifold $V$ inherits an action of the circle group $\T$. When $V$ has an almost-complex structure, the tangent bundle of the free loopspace, pulled back to a certain infinite cyclic cover $\LV$, has an equivariant decomposition as a completion of $\bT V \otimes (\oplus \C(k))$, where $\bT V$ is an equivariant bundle on the cover, nonequivariantly isomorphic to the pullback of $TV$ along evaluation at the basepoint (and $\oplus \C(k)$ denotes an algebra of Laurent polynomials). On a flat manifold, this analogue of Fourier analysis is classical.

Citation

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Jack Morava. "The tangent bundle of an almost-complex free loopspace." Homology Homotopy Appl. 3 (2) 407 - 415, 2001.

Information

Published: 2001
First available in Project Euclid: 13 February 2006

zbMATH: 1035.58009
MathSciNet: MR1856034

Subjects:
Primary: 58B25
Secondary: 53C29, 55P91

Rights: Copyright © 2001 International Press of Boston

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Vol.3 • No. 2 • 2001
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