The DOI matches its Crossref record; 7 of the 7 references it cites were found in a registry or an index.
Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem
Open accessAbstract
Abstract:In this paper we solve a longstanding internal problem of noncommutative geometry, namely the computation of the index of transversally elliptic operators on foliations. We show that the computation of the local index formula for transversally hypoelliptic operators can be settled thanks to a very specific Hopf algebra , associated to each integer codimension. This Hopf algebra reduces transverse geometry, to a universal geometry of affine nature. The structure of this Hopf algebra, its relation with the Lie algebra of formal vector fields as well as the computation of its cyclic cohomology are done in the present paper, in which we also show that under a suitable unimodularity condition the cosimplicial space underlying the Hochschild cohomology of a Hopf algebra carries a highly nontrivial cyclic structure.
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Cites
Connes, A., Cuntz, J., & Rieffel, M. A. (2010) · Oberwolfach Reports · doi:10.4171/owr/2009/41 · Cited by 2,268
Self-citationFoundations of Quantum Group Theory
Majid, S. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511613104 · Cited by 1,940
Quantum groups and non-commutative geometry
Manin, I. I. (1988) · Medical Entomology and Zoology · Cited by 695
The Local Index Formula in Noncommutative Geometry
Connes, A., & Moscovici, H. (1995) · Birkhäuser Basel eBooks · doi:10.1007/978-3-0348-9102-8_4 · Cited by 388
Self-citationCyclic cohomology, the Novikov conjecture and hyperbolic groups
Connes, A., & Moscovici, H. (1990) · Topology · doi:10.1016/0040-9383(90)90003-3 · Cited by 357
Self-citationThe local index formula in noncommutative geometry
Connes, A., & Moscovici, H. (1995) · Geometric and Functional Analysis · doi:10.1007/bf01895667 · Cited by 306
Self-citationSur les classes caractéristiques des feuilletages
Haefliger, A. (1973) · Lecture notes in mathematics · doi:10.1007/bfb0069285 · Cited by 38
Cited by
Hopf Algebras, Renormalization and Noncommutative Geometry
Connes, A., & Kreimer, D. (1998) · Communications in Mathematical Physics · doi:10.1007/s002200050499 · Cited by 786
Self-citationCartier, P. (2007) · Frontiers in Number Theory, Physics, and Geometry II · doi:10.1007/978-3-540-30308-4_12 · Cited by 145
Quantum groups and noncommutative geometry
Majid, S. (2000) · Journal of Mathematical Physics · doi:10.1063/1.533331 · Cited by 92
Metadata
- Authors
- Connes, A., & Moscovici, H.
- Venue
- Communications in Mathematical Physics
- Published
- 1998-11-01
- Volume
- 198
- Issue
- 1
- Pages
- 199-246
- ISSN
- 0010-3616 (ISSN-L)
- 1432-0916
- OpenAlex
- W1970398487
- Cited by
- 330
- References
- 7
- FWCI
- 28.64
- Type
- journal article
- Language
- en
- Open access
- green
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- Connes, A., & Moscovici, H. (1998). Hopf Algebras, Cyclic Cohomology and the Transverse Index Theorem. Communications in Mathematical Physics. https://doi.org/10.1007/s002200050477
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