# Seminário Geometria em Lisboa

### Circle invariant definite connections and symplectic Fano 6-manifolds.

I will describe work in progress, joint with Dmitri Panov. A definite connection is an $SO(3)$-connection over a $4$-manifold, whose curvature is non-zero on every tangent $2$-plane. Given such a connection, the associated $2$-sphere bundle is naturally a symplectic manifold. In this talk I will be interested in definite connections invariant under a circle action, in which case the corresponding symplectic six-manifold is “Fano". I will explain how we hope to classify them, the only possibilities should be connections over $S^4$ or $\operatorname{CP}^2$ giving Fanos $\operatorname{CP}^3$ and the complete flag on $C^3$ respectively.

Organizador corrente: Rosa Sena Dias

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