Index theory groupoids

Keywords: groupoid C*-algebra, manifold with singularities, Z/k-manifold, elliptic operator, KK-theory, index theorem, positive scalar curvature. Mathematics 

17 Jan 2019 Fibrewise equivariant compactifications under étale groupoid actions, Preprint version: pdf. The Varied Landscape of Operator Theory, Main Index Algebraic structures Structures with one operation Groupoids of groupoid introduced by Heinrich Brandt and used in the category theory and  22 Aug 2017 Mathematical approaches to Quantum Field Theory, such as Conformal Field Theory and The index of geometric operators on Lie groupoids. Groupoid. There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator.

[50] Monthubert B., Groupoids of manifolds with corners and index theory, in: Groupoids in Analysis, Geometry, and Physics (Boulder, CO, 1999), Contemp.

1 Microlocal methods in quantum field theory (Bahns, Schrohe, Witt) from harmonic analysis and index theory for certain invariant differential operators is at Some conditions may be imposed on the groupoid: if it has a finite unit space , the  17 Jan 2019 Fibrewise equivariant compactifications under étale groupoid actions, Preprint version: pdf. The Varied Landscape of Operator Theory, Main Index Algebraic structures Structures with one operation Groupoids of groupoid introduced by Heinrich Brandt and used in the category theory and  22 Aug 2017 Mathematical approaches to Quantum Field Theory, such as Conformal Field Theory and The index of geometric operators on Lie groupoids. Groupoid. There are at least three definitions of "groupoid" currently in use. The first type of groupoid is an algebraic structure on a set with a binary operator. Atiyah-Singer index theorem using the tangent groupoid and groupoid techniques. As he notes, his proof is closely related to the K-theory proof of Atiyah and  13 Aug 2016 generalization of Atiyah-Singer index theory, is to study the conjecture in its more general form, as stated for Lie groupoids (i.e. groupoids 

Index theory and Groupoids . By Claire Debord and Jean-Marie Lescure. Abstract. This paper collects the notes of a serie of lectures given by the two authors during the summer school "Geometric and topological methods for Quantum Field Theory" at Villa de Leyva, Colombia, summer 2007. These lecture notes are mainly devoted to a proof using

the ''right class of pseudodifferential operators'' for index theory on singular tion 3 is devoted to the construction of tangent spaces and tangent groupoids 

Index theory and groupoids

17 Sep 2008 These lecture notes are mainly devoted to a proof using groupoids and. KK- theory of Atiyah and Singer's index theorem on compact smooth 

A different but related direction is to extend this theory to singular spaces [3]. An important step in the index problem on singular manifolds was made by Melrose [  

The Higson-Roe sequence for étale groupoids II. Our construction allows to couple the K-theory analytic indices of L-projective leafwise elliptic operators with   29 May 2017 index theory understood in a broad sense (cohomological and analytical methods, secondary invariants, K-theory, C^*-algebras, groupoids,  groupoid G and index theory of pseudodifferential operators. The second ap- plication is to operators on a covering ˜. M of a manifold with boundary M, with. 1 Microlocal methods in quantum field theory (Bahns, Schrohe, Witt) from harmonic analysis and index theory for certain invariant differential operators is at Some conditions may be imposed on the groupoid: if it has a finite unit space , the 

ical index map can be described with the use of a groupoid, namely a deformation groupoid. This approach has been extented by the authors and V. Nistor [20] who showed that the topological index of Atiyah-Singer can also be described using deformation groupoids. This leads to a geometrical proof of the index theorem of