K-homology and index theory on contact manifolds

Paul Frank Baum, Erik van Erp

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)1-48
Number of pages48
JournalActa Mathematica
Volume213
Issue number1
DOIs
StatePublished - Sep 1 2014

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K-homology
Contact Manifold
Index Theory
Fredholm Operator
Hypoelliptic Operators
Index Theorem
K-theory
Elliptic Operator
Calculus
Cycle
Calculate

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Baum, Paul Frank ; van Erp, Erik. / K-homology and index theory on contact manifolds. In: Acta Mathematica. 2014 ; Vol. 213, No. 1. pp. 1-48.
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K-homology and index theory on contact manifolds. / Baum, Paul Frank; van Erp, Erik.

In: Acta Mathematica, Vol. 213, No. 1, 01.09.2014, p. 1-48.

Research output: Contribution to journalArticle

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