Khavkine I. Applications of compatibility complexes and their cohomology in relativity and gauge theories, talk at The Workshop on Integrable Nonlinear Equations, 18-24 October 2015, Mikulov, Czech Republic (abstract): Difference between revisions
Created page with "{{MeetingTalk | speaker = Igor Khavkine | title = Applications of compatibility complexes and their cohomology in relativity and gauge theories | abstract = I will discuss the..." |
No edit summary |
||
| Line 3: | Line 3: | ||
| title = Applications of compatibility complexes and their cohomology in relativity and gauge theories | | title = Applications of compatibility complexes and their cohomology in relativity and gauge theories | ||
| abstract = I will discuss the Killing operator (<math>K_{ab}[v] = \nabla_a v_b + \nabla_b v_a</math>) as an overdetermined differential operator and its (formal) compatibility complex. It has been recently observed that this compatibility complex and its cohomology play an important role in General Relativity. In more general gauge theories, an analogous role is played by the "gauge generator" operator and its compatibility complex. An important open problem is to explicitly compute the tensorial form of the compatibility complex on (pseudo-)Riemannian spaces of special interest. Surprisingly, despite its importance, the full compatibility complex is known in only very few cases. I have recently reviewed one of these cases, constant curvature spaces, where this complex is known as the Calabi complex, in {{arXiv|1409.7212}}. | | abstract = I will discuss the Killing operator (<math>K_{ab}[v] = \nabla_a v_b + \nabla_b v_a</math>) as an overdetermined differential operator and its (formal) compatibility complex. It has been recently observed that this compatibility complex and its cohomology play an important role in General Relativity. In more general gauge theories, an analogous role is played by the "gauge generator" operator and its compatibility complex. An important open problem is to explicitly compute the tensorial form of the compatibility complex on (pseudo-)Riemannian spaces of special interest. Surprisingly, despite its importance, the full compatibility complex is known in only very few cases. I have recently reviewed one of these cases, constant curvature spaces, where this complex is known as the Calabi complex, in {{arXiv|1409.7212}}. | ||
| slides = | | slides = Media:Khavkine I. Applications of compatibility complexes and their cohomology in relativity and gauge theories (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf | ||
| references = | | references = | ||
| 79YY-MM-DD = 7984-89-81 | | 79YY-MM-DD = 7984-89-81 | ||
}} | }} | ||
Revision as of 11:45, 3 November 2015
Speaker: Igor Khavkine
Title: Applications of compatibility complexes and their cohomology in relativity and gauge theories
Abstract:
I will discuss the Killing operator () as an overdetermined differential operator and its (formal) compatibility complex. It has been recently observed that this compatibility complex and its cohomology play an important role in General Relativity. In more general gauge theories, an analogous role is played by the "gauge generator" operator and its compatibility complex. An important open problem is to explicitly compute the tensorial form of the compatibility complex on (pseudo-)Riemannian spaces of special interest. Surprisingly, despite its importance, the full compatibility complex is known in only very few cases. I have recently reviewed one of these cases, constant curvature spaces, where this complex is known as the Calabi complex, in arXiv:1409.7212.
![{\displaystyle K_{ab}[v]=\nabla _{a}v_{b}+\nabla _{b}v_{a}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cd00c3dcefd727bc689cf91a243e3e2542b44f2d)
Slides: Media:Khavkine I. Applications of compatibility complexes and their cohomology in relativity and gauge theories (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).pdf