Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-28T15:33:32.710Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive Curvature, Partial Vanishing Theorems and Coarse Indices

Part of: $K$-theory and operator algebras Partial differential equations on manifolds; differential operators

Published online by Cambridge University Press:  22 July 2015

John Roe
John Roe*
Affiliation:
Department of Mathematics, Penn State University, University Park, PA 16802, USA ([email protected])
Get access Rights & Permissions [Opens in a new window]

Abstract

We generalize the relative index theorem of Gromov and Lawson, using coarse geometry.

Keywords

index theoremWeitzenbock formulacoarse geometry

MSC classification

Secondary: 58J22: Exotic index theories 19K56: Index theory
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 223 - 233
Copyright
Copyright © Edinburgh Mathematical Society 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Gromov, M. and Lawson, H. B., Positive scalar curvature and the Dirac operator on complete Riemannian manifolds, Publ. Math. IHES 58(1) (1983), 83–196.Google Scholar
2. Higson, N. and Roe, J., Analytic K-homology, Oxford Mathematical Monographs (Oxford University Press, 2000).Google Scholar
3. Higson, N., Roe, J. and Yu, G., A coarse Mayer–Vietoris principle, Math. Proc. Camb. Phil. Soc. 114 (1993), 85–97.CrossRefGoogle Scholar
4. Lichnerowicz, A., Spineurs harmoniques, C. R. Acad. Sci. Paris Sér. I 257 (1963), 7–9 (in French).Google Scholar
5. Roe, J., Partitioning non-compact manifolds and the dual Toeplitz problem, in Operator algebras and applications (ed. Evans, D. and Takesaki, M.), pp. 187–228 (Cambridge University Press, 1989).CrossRefGoogle Scholar
6. Roe, J., A note on the relative index theorem, Q. J. Math. 42 (1991), 365–373.Google Scholar
7. Roe, J., Index theory, coarse geometry, and the topology of manifolds, CBMS Conference Proceedings, Volume 90 (American Mathematical Society, Providence, RI, 1996).Google Scholar
8. Roe, J. and Siegel, P., Sheaf theory and Paschke duality, K-Theory 12 (2013), 213–234.Google Scholar
9. Siegel, P., Homological calculations with analytic structure groups, PhD thesis, Penn State (2012).Google Scholar