Bott periodicity for fibred cusp operators
Date
2005
Authors
Rochon, Frédéric
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Publisher
American Mathematical Society
Abstract
In the framework of fibred cusp operators on a manifold X associated to a boundary fibration Φ: ∂X → Y, the homotopy groups of the space Gᵩ⁻∞ (X; E) 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 Kc⁰ (T*Y).
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Source
Journal of Geometric Analysis
Type
Journal article