Toric Contact Manifolds

Prof. Dr. Miguel Abreu (Universidade de Lisboa)

Thursday, 25 May, 14:00-16:00, HG G 19.2
Tuesday, 30 May, 14:00-16:00, HG F 26.3
Thursday, 1 June, 14:00-16:00, HG F 26.3
Monday, 5 June, 10:00 to 12:00, HG G 19.2
Wednesday, 7 June, 10:00 to 12:00, HG G 19.2

Abstract

Toric contact manifolds provide an interesting class of contact manifolds. In this mini-course we will introduce them, show how the ones with zero first Chern class can be determined by certain integral convex polytopes, called toric diagrams, and how to directly read relevant contact invariants from these toric diagrams. Plenty of hands-on examples and some applications will be provided.

References:

M. Abreu and L. Macarini. Contact homology of good toric contact manifolds. Compos. Math., 148 (2012), 304–334.

M. Abreu and L. Macarini. On the mean Euler characteristic of Gorenstein toric contact manifolds. Int. Math. Res. Not. IMRN, 14 (2020), 4465–4495.

M. Abreu, L. Macarini and M. Moreira. On contact invariants of non-simply connected Gorenstein toric contact manifolds. Mathematical Research Letters, 29 (2022), 1-42

M. Abreu, L. Macarini and M Moreira. Contact invariants of Q-Gorenstein toric contact manifolds, the Ehrhart polynomial and Chen-Ruan cohomology. Preprint (2022), arXiv:2202.00442.

A. Cannas da Silva. Symplectic toric manifolds, in "Symplectic geometry of integrable Hamiltonian systems" (Barcelona, 2001), 85–173, 2003.

E. Lerman. Contact toric manifolds. J. Symplectic Geom., 1 (2003), 785–828, 2003.