## Acta Mathematica

### K-homology and index theory on contact manifolds

#### Abstract

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 calculate the K-cycle (i.e., the element in geometric K-homology) determined by any hypoelliptic Fredholm operator in the Heisenberg calculus.

The index theorem of this paper precisely indicates how the analytic versus geometric K-homology setting provides an effective framework for extending formulas of Atiyah–Singer type to non-elliptic Fredholm operators.

#### Note

Paul Baum thanks Dartmouth College for the generous hospitality provided to him via the Edward Shapiro fund. Erik van Erp thanks Penn State University for a number of productive and enjoyable visits. PFB was partially supported by NSF grant DMS-0701184. EvE was partially supported by NSF grant DMS-1100570.

#### Dedication

With admiration and affection we dedicate this paper to Sir Michael Atiyah on the occasion of his 85th birthday.

#### Article information

Source
Acta Math., Volume 213, Number 1 (2014), 1-48.

Dates
First available in Project Euclid: 30 January 2017

https://projecteuclid.org/euclid.acta/1485801834

Digital Object Identifier
doi:10.1007/s11511-014-0114-5

Mathematical Reviews number (MathSciNet)
MR3261009

Zentralblatt MATH identifier
1323.58017

Rights

#### Citation

Baum, Paul F.; Erp, Erik. K -homology and index theory on contact manifolds. Acta Math. 213 (2014), no. 1, 1--48. doi:10.1007/s11511-014-0114-5. https://projecteuclid.org/euclid.acta/1485801834

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