arXiv math/04082252004-08math.DGmath.AP

Bott Periodicity for Fibred Cusp Operators

Frederic Rochon

备注：: 38 pages, corrected typos

英文摘要：

In the framework of fibred cusp operators on a manifold $X$ associated to a boundary fibration $Φ: \pa X\to Y$, the homotopy groups of the space of invertible smoothing perturbations of the identity are computed in terms of the K-theory of $T^{*}Y$. It is shown that there is a periodicity, namely the odd and the even homotopy groups are isomorphic among themselves. To obtain this result, one of the important steps is the description of the index of a Fredholm smoothing perturbation of the identity in terms of an associated K-class in the K-theory of $T^{*}Y$.

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