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.
Funding Statement
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.
Citation
Paul F. Baum. Erik Erp. "K-homology and index theory on contact manifolds." Acta Math. 213 (1) 1 - 48, 2014. https://doi.org/10.1007/s11511-014-0114-5
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