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

Abstract

Kollár has found subtle obstructions to the existence of Sasakian structures on 5-dimensional manifolds. In the present article we develop methods of using these obstructions to distinguish K-contact manifolds from Sasakian ones. In particular, we find the first example of a closed 5-manifold M with $H_1(M,Z)=0$ which is K-contact but which carries no semi-regular Sasakian structures.

31 pages, no figures; v2. small correction in the proof of Theorem 32

References in corpus (2)

• Symplectic resolutions, Lefschetz property and formality
• A non-Sasakian Lefschetz K-contact manifold of Tievsky type

Cited by in corpus (3)

• Resolving symplectic orbifolds with applications to finite group actions
• A non-Sasakian Lefschetz K-contact manifold of Tievsky type
• Negative Sasakian structures on simply-connected 5-manifolds