Room 217

Homology Smale-Barden manifolds with K-contact and Sasakian structures

Aleksy Tralle

University of Warmia and Mazury, Olsztyn

The talk is devoted to a problem of finding 1-connected manifolds
with K-contact structures which do not admit Sasakian structures in
dimension 5. This question (posed by Boyer and Galicki) should be considered
as an odd-dimensional version of the topic "symplectic versus Kaehler". The
answer to the question is positive in dimensions greater or equal to 7 (the
works of the author together with Biswas, Fernandez, Hajduk and Munoz). In
dimension 5 the problem is much more complicated, since the methods of
homotopy theory do not work anymore. We prove a weaker version of the result
constructing closed manifold with the vanishing first homology group, which
admits K-contact structures but no Sasakian structures. Our approach uses
methods of symplectic topology and algebraic geometry. Joint work with
Vicente Munoz and Juan Angel Rojo.