Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Rouse, Paulo Carrillo"'
We give a complete solution, for discrete countable groups, to the problem of defining and computing a geometric pairing between the left hand side of the Baum-Connes assembly map, given in terms of geometric cycles associated to proper actions on ma
Externí odkaz:
http://arxiv.org/abs/2012.12359
Publikováno v:
Ann. K-Th. 6 (2021) 607-628
Given a connected manifold with corners of any codimension there is a very basic and computable homology theory called conormal homology defined in terms of faces and orientations of their conormal bundles, and whose cycles correspond geometrically t
Externí odkaz:
http://arxiv.org/abs/1910.11049
Autor:
Akrour, Ibrahim, Rouse, Paulo Carrillo
Using recently introduced Debord-Skandalis Blup's groupoids we study index theory for a compact foliated manifold with boundary inducing a foliation in its boundary. For this we consider first a blup groupoid whose Lie algebroid has sections consisti
Externí odkaz:
http://arxiv.org/abs/1711.11197
Publikováno v:
Ann. K-Th. 3 (2018) 523-563
For every connected manifold with corners we use a homology theory called conormal homology, defined in terms of faces and incidences and whose cycles correspond geometrically to corner's cycles. Its Euler characteristic (over the rationals, dimensio
Externí odkaz:
http://arxiv.org/abs/1703.05612
Autor:
Rouse, Paulo Carrillo
The goal of this paper is to construct a calculus whose higher indices are naturally elements in the twisted K-theory groups for Lie groupoids. Given a Lie groupoid $G$ and a $PU(H)$-valued groupoid cocycle, we construct an algebra of projective pseu
Externí odkaz:
http://arxiv.org/abs/1602.08370
Using a combination of Atiyah-Segal ideas on one side and of Connes and Baum-Connes ideas on the other, we prove that the Twisted geometric K-homology groups of a Lie groupoid have an external multiplicative structure extending hence the external pro
Externí odkaz:
http://arxiv.org/abs/1501.05255
Autor:
Rouse, Paulo Carrillo, Wang, Bai-Ling
Publikováno v:
Ann. Scient. \'Ec. Norm. Sup. 4e s\'erie t.49, 2016, p. 305 \`a 351
We construct the geometric Baum-Connes assembly map for twisted Lie groupoids, that means for Lie groupoids together with a given groupoid equivariant $PU(H)-$principle bundle. The construction is based on the use of geometric deformation groupoids,
Externí odkaz:
http://arxiv.org/abs/1402.3456
We give a cohomological formula for the index of a fully elliptic pseudodifferential operator on a manifold with boundary. As in the classic case of Atiyah-Singer, we use an embedding into an euclidean space to express the index as the integral of a
Externí odkaz:
http://arxiv.org/abs/1207.3514
Autor:
Rouse, Paulo Carrillo, Wang, Bai-Ling
For a Lie groupoid G with a twisting (a PU(H)-principal bundle over G), we use the (geometric) deformation quantization techniques supplied by Connes tangent groupoids to define an analytic index morphism in twisted K-theory. In the case the twisting
Externí odkaz:
http://arxiv.org/abs/1005.3842
In his book (II.5), Connes gives a proof of the Atiyah-Singer index theorem for closed manifolds by using deformation groupoids and appropiate actions of these on R^N. Following these ideas, we prove an index theorem for manifolds with boundary.
Externí odkaz:
http://arxiv.org/abs/0905.1420