Title: Towards Topological Invariants and the Theory of Gravity on Noncommutative Spaces

Speaker: Octavio Obregón

Institution: Instituto de Física, Univeridad de Guanajuato, León, Gto. México

Abstract

Pontrjagin and Euler topological invariants on noncommutative spaces arise in a similar manner as noncommutative Yang-Mills theories. We make use of the Seiberg-Witten map to show how these noncommutative topological invariants can be constructed based on a SL(2,C) complex connection. The same procedure is followed to define a theory of gravity on noncommutative spaces. We speculate on the description of noncommutative gravitational instantons. Our procedure is not diffeomorphism invariant. It has been recently claimed that a noncommutative gravitational theory can be constructed based on a twisted Poincaré algebra. We briefly comment on this proposal in connection with our results. (Most of this work has been realized and published with H. García-Compean, C. Ramírez and M. Sabido).