The first instances of deformation theory were given by Kodaira and Spencer for complex structures and by Gerstenhaber for associative algebras. Since then, deformation theory has been applied as a useful tool in the study of many other mathematical structures, and even today it plays an important role in many developments of modern mathematics. This volume collects a few self-contained and peer-reviewed papers by experts which present up-to-date research topics in algebraic and motivic topology, quantum field theory, algebraic geometry, noncommutative geometry and the deformation theory of Poisson algebras. They originate from activities at the Max-Planck-Institute for Mathematics and the Hausdorff Center for Mathematics in Bonn.
Author(s): Hossein Abbaspour, Matilde Marcolli, Thomas Tradler (eds.)
Publisher: Vieweg+Teubner
Year: 2010
Language: English
Pages: 182
Cover......Page 1
Deformation
Spaces......Page 3
ISBN 9783834812711......Page 4
Preface......Page 6
Contents......Page 8
On the Hochschild and Harrison (co)homology of C∞-algebras and applications to string topology
......Page 10
1. Hochschild (co)homology of an A8-algebra with values in a bimodule......Page 13
2. C∞-algebras, C∞-bimodules, Harrison (co)homology
......Page 19
3. λ-operations and Hodge decomposition
......Page 26
4. An exact sequence `a laJacobi-Zariski
......Page 40
5. Applications to string topology......Page 50
References......Page 58
1. Introduction......Page 62
2. Open abelian varieties......Page 65
3. Gluing and SPCMC structure......Page 70
4. The Jacobian of a worldsheet with boundary......Page 75
5. The lattice conformal .eld theory on the SPCMC of open abelian varieties......Page 80
References......Page 82
1. Introduction......Page 84
2. Preliminary
......Page 85
3. Weight on pseudo-coherent Modules......Page 91
4. Proof of the main theorem......Page 92
5. Applications......Page 96
References......Page 97
1. Introduction......Page 100
2. Index theory for Lie groupoids
......Page 103
3. Index theory and strict deformation quantization
......Page 109
4. Higher localized indices......Page 114
References......Page 119
Introduction......Page 122
1. Review of DGLAs and L∞-algebras
......Page 124
2. The Thom-Whitney complex......Page 127
3. Semicosimplicial differential graded Lie algebras and mapping cones......Page 130
4. Semicosimplicial Cartan homotopies......Page 133
5. Semicosimplicial Lie algebras and deformations of smooth varieties......Page 135
6. Proof of the main theorem......Page 137
References......Page 140
1. Introduction......Page 144
2. Linear algebra......Page 146
References......Page 150
1. Introduction......Page 152
2. Preliminaries: L∞-algebras and Poisson algebras
......Page 156
3. Choice in a transfer of L∞-algebra structure......Page 162
4. Deformations of Poisson structures via L∞-algebras......Page 172
References......Page 181
