منابع مشابه
Cobordism Invariance of the Index
We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on σ-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of a manifold X has a suitable extension to K1(TX), then its index is zero. This con...
متن کاملCobordism invariance of the family index
We give a K-theory proof of the invariance under cobordism of the family index. We consider elliptic pseudodifferential families on a continuous fibre bundle with smooth fibres M →֒ M → B, and define a notion of cobordant families using K-groups on fibrations with boundary. We show that the index of two such families is the same using properties of the push-forward map in K-theory to reduce it t...
متن کاملCusp geometry and the cobordism invariance of the index
The cobordism invariance of the index on closed manifolds is reproved using the calculus Ψc of cusp pseudodifferential operators on a manifold with boundary. More generally, on a compact manifold with corners, the existence of a symmetric cusp differential operator of order 1 and of Dirac type near the boundary implies that the sum of the indices of the induced operators on the hyperfaces is null.
متن کاملCobordism Invariance of the Index of a Transversally Elliptic Operator
1. The SpinC-Dirac operator and the SpinC-quantization In this section we reformulate the “SpinC-quantization commutes with cobordism” principal in a more analytic language. In Subsection 1.1, we briefly recall the notion of SpinC-Dirac operator. We refer the reader to [2, 6] for details. We also express the SpinC-quantization of an orbifold M = X/G in terms of the index of the lift of the Spin...
متن کاملOn the Cobordism Invariance of the Index of Dirac Operators
We describe a “tunneling” proof of the cobordism invariance of the index of Dirac operators. The goal of this note is to present a very short proof of the cobordism invariance of the index. More precisely, if D̂ is a Dirac operator on an odd dimensional manifold M̂ with boundary ∂M̂ = M then we show that the index of its restriction D to M is zero. The novelty of this proof consists in the fact th...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2009
ISSN: 0166-8641
DOI: 10.1016/j.topol.2009.03.003