K-homology and Fredholm operators I: Dirac operators

@article{Baum2018KhomologyAF,
  title={K-homology and Fredholm operators I: Dirac operators},
  author={Paul Frank Baum and Erik van Erp},
  journal={Journal of Geometry and Physics},
  year={2018}
}
  • P. Baum, E. Erp
  • Published 12 April 2016
  • Mathematics
  • Journal of Geometry and Physics

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References

SHOWING 1-10 OF 25 REFERENCES

K-homology and Fredholm Operators II: Elliptic Operators

This is an expository paper which gives a proof of the Atiyah-Singer index theorem for elliptic operators. Specifcally, we compute the geometric K-cycle that corresponds to the analytic K-cycle

K-homology and index theory on contact manifolds

This paper applies K-homology to solve the index problem for a class of hypoelliptic (but not elliptic) operators on contact manifolds. K-homology is the dual theory to K-theory. We explicitly

Heat Kernels and Dirac Operators

The past few years have seen the emergence of new insights into the Atiyah-Singer Index Theorem for Dirac operators. In this book, elementary proofs of this theorem, and some of its more recent

A note on the cobordism invariance of the index

CLIFFORD MODULES

  • A.
  • Mathematics
  • 1964
The purpose of the paper is to undertake a detailed investigation of the role of Clifford algebras and spinors in the K&theory of real vector bundles. On the one hand the use of Clifford algebras

Spectral asymmetry and Riemannian geometry. III

In Parts I and II of this paper ((4), (5)) we studied the ‘spectral asymmetry’ of certain elliptic self-adjoint operators arising in Riemannian geometry. More precisely, for any elliptic self-adjoint

Spectral asymmetry and Riemannian Geometry. I

1. Introduction. The main purpose of this paper is to present a generalization of Hirzebruch's signature theorem for the case of manifolds with boundary. Our result is in the framework of Riemannian

Characteristic Classes

Let (P,M,G) be a principle fibre bundle over M with group G, connection ω and quotient map π. Recall that for all p ∈ P the Lie algebra G is identified with VpP := Kerπp∗ via the derivative of lp : G

Topology from the differentiable viewpoint

Preface1Smooth manifolds and smooth maps1Tangent spaces and derivatives2Regular values7The fundamental theorem of algebra82The theorem of Sard and Brown10Manifolds with boundary12The Brouwer fixed

Seminar on the Atiyah-Singer Index Theorem.

The description for this book, Seminar on Atiyah-Singer Index Theorem. (AM-57), will be forthcoming.