## 7 Citations

### Index theory and noncommutative geometry: a survey

- MathematicsAdvances in Noncommutative Geometry
- 2019

This chapter is an introductory survey of selected topics in index theory in the context of noncommutative geometry, focusing in particular on Alain Connes’ contributions. This survey has two parts.…

### The Index Theorem for Toeplitz Operators as a Corollary of Bott Periodicity

- Mathematics
- 2020

This is an expository paper about the index of Toeplitz operators, and in particular Boutet de Monvel's theorem. We prove Boutet de Monvel's theorem as a corollary of Bott periodicity, and…

### Some geometric results on K-theory with $${\mathbb{Z}}/k{\mathbb{Z}}$$-coefficients

- Mathematics
- 2020

We establish some geometric results on K-theory with coefficients in
$${\mathbb{Z}}/k{\mathbb{Z}}$$
. The first one is a new proof of the Atiyah–Patodi–Singer mod k index theorem (Math Proc Camb…

### A new proof of an index theorem of Freed and Melrose

- Mathematics
- 2020

In this note we establish a new geometric proof of a mod k index formula of Freed and Melrose. Applications are given as well.

## References

SHOWING 1-10 OF 25 REFERENCES

### K-homology and Fredholm Operators II: Elliptic Operators

- Mathematics
- 2016

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

- Mathematics
- 2011

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

- Mathematics
- 1992

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…

### CLIFFORD MODULES

- 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

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1976

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

- MathematicsMathematical Proceedings of the Cambridge Philosophical Society
- 1975

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

- Mathematics
- 2004

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

- Mathematics
- 1965

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.

- Mathematics
- 1968

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