Details
| Originalsprache | Englisch |
|---|---|
| Aufsatznummer | 104128 |
| Fachzeitschrift | Journal of geometry and physics |
| Jahrgang | 163 |
| Frühes Online-Datum | 15 Feb. 2021 |
| Publikationsstatus | Veröffentlicht - Mai 2021 |
Abstract
We introduce and study the index morphism for leafwise G-transversally elliptic operators on smooth closed foliated manifolds. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes–Skandalis index class of the corresponding leafwise elliptic operators on the quotient foliation. Finally we prove the compatibility of our index morphism with the Gysin morphism and reduce its computation to the case of tori actions. We also construct a topological candidate for an index theorem using the Kasparov–Dirac element for euclidean G-representations.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Mathematische Physik
- Physik und Astronomie (insg.)
- Mathematik (insg.)
- Geometrie und Topologie
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in: Journal of geometry and physics, Jahrgang 163, 104128, 05.2021.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - The index of leafwise G-transversally elliptic operators on foliations
AU - Baldare, Alexandre
AU - Benameur, Moulay Tahar
N1 - Funding Information: The authors wish to thank A. Carey, P. Carrillo-Rouse, T. Fack, J. Heitsch, M. Hilsum, P. Hochs, Y. Kordyukov, V. Mathai, H. Oyono-Oyono, V. Nistor, S. Paycha, M. Puschnigg, A. Rennie and G. Skandalis for many helpful discussions. Part of this work was realized during the postdoctoral position of the first author in the Institut Elie Cartan de Lorraine at Metz, he is indebted to the members of the noncommutative geometry team for the warm hospitality. The second author would like to thank his colleagues in Montpellier, and more specifically P.-E. Paradan, for several interesting conversations around transversally elliptic operators and their applications. Both authors thank the French National Research Agency, France for the financial support via the ANR-14-CE25-0012-01 (SINGSTAR).
PY - 2021/5
Y1 - 2021/5
N2 - We introduce and study the index morphism for leafwise G-transversally elliptic operators on smooth closed foliated manifolds. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes–Skandalis index class of the corresponding leafwise elliptic operators on the quotient foliation. Finally we prove the compatibility of our index morphism with the Gysin morphism and reduce its computation to the case of tori actions. We also construct a topological candidate for an index theorem using the Kasparov–Dirac element for euclidean G-representations.
AB - We introduce and study the index morphism for leafwise G-transversally elliptic operators on smooth closed foliated manifolds. We prove the usual axioms of excision, multiplicativity and induction for closed subgroups. In the case of free actions, we relate our index class with the Connes–Skandalis index class of the corresponding leafwise elliptic operators on the quotient foliation. Finally we prove the compatibility of our index morphism with the Gysin morphism and reduce its computation to the case of tori actions. We also construct a topological candidate for an index theorem using the Kasparov–Dirac element for euclidean G-representations.
KW - Foliation
KW - Fredholm index
KW - Group action
KW - K-homology
KW - KK-theory
KW - Transversally elliptic
UR - http://www.scopus.com/inward/record.url?scp=85101310421&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2001.02428
DO - 10.48550/arXiv.2001.02428
M3 - Article
AN - SCOPUS:85101310421
VL - 163
JO - Journal of geometry and physics
JF - Journal of geometry and physics
SN - 0393-0440
M1 - 104128
ER -