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Adiabatic groupoid and secondary invariants in K-theory.
- Source :
-
Advances in Mathematics . Apr2019, Vol. 347, p940-1001. 62p. - Publication Year :
- 2019
-
Abstract
- Abstract In this paper we define new K-theoretic secondary invariants attached to a Lie groupoid G. The receptacle for these invariants is the K-theory of C r ⁎ (G a d ∘) (where G a d ∘ is the adiabatic deformation G restricted to the interval [ 0 , 1)). Our construction directly generalises the cases treated in [29,30] , in the setting of the Coarse Geometry, to more involved geometrical situations, such as foliations. Moreover we tackle the problem of producing a wrong-way functoriality between adiabatic deformation groupoid K-groups associated to transverse maps. This extends the construction of the lower shriek map in [6]. Furthermore we prove a Lie groupoid version of the Delocalized APS Index Theorem of Piazza and Schick. Finally we give a product formula for secondary invariants. [ABSTRACT FROM AUTHOR]
- Subjects :
- *K-theory
*GEOMETRY
*FOLIATIONS (Mathematics)
*CONTAINERS
Subjects
Details
- Language :
- English
- ISSN :
- 00018708
- Volume :
- 347
- Database :
- Academic Search Index
- Journal :
- Advances in Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 135578347
- Full Text :
- https://doi.org/10.1016/j.aim.2019.03.003