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On Seiberg-Witten equationsοn symplectic 4-manifolds

Klaus Mohnke (1997)

Banach Center Publications

We discuss Taubes' idea to perturb the monopole equations on symplectic manifolds to compute the Seiberg-Witten invariants in the light of Witten's symmetry trick in the Kähler case.

On Sp(2) and Sp(2) · Sp(1) structures in 8-dimensional vector bundles.

Martin Cadek, Jirí Vanzura (1997)

Publicacions Matemàtiques

Let ξ be an oriented 8-dimensional vector bundle. We prove that the structure group SO(8) of ξ can be reduced to Sp(2) or Sp(2) · Sp(1) if and only if the vector bundle associated to ξ via a certain outer automorphism of the group Spin(8) has 3 linearly independent sections or contains a 3-dimensional subbundle. Necessary and sufficient conditions for the existence of an Sp(2)- structure in ξ over a closed connected spin manifold of dimension 8 are also given in terms of characteristic classes.

On the topology of positively curved Bazaikin spaces

Luis A. Florit, Wolfgang Ziller (2009)

Journal of the European Mathematical Society

We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact,...

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