Abstract:

Abstract: Let X be a topological space and \tau an involution of X; \tau induces an action of the group G = { id, \tau} on X. A particular case is when X is a complex manifold and \tau is the complex conjugation; there some algebraic relations between the rings H*(X), H*(X^G) and H*_G(X) occur, where X^G denotes the fixed point subspace and H*_G(X) the G-equivariant cohomology ring of X. Such relations motivate the definition of cohomology frame and allow us to generalize the notion of complex conjugation to another topological spaces. Therefore, we say that a Conjugation Space is a space with involution which admits a cohomology frame. In this talk the notion of conjugation space is introduced, and some properties and examples of such spaces are presented.