Hauptseminar Symplektische Geometrie

H-holomorphic curves are solutions of a specific modification of the pseudoholomorphic curve equation in symplectizations involving a harmonic 1-form as perturbation term. This modification of the pseudoholomorphic curve equation was first suggested by Hofer [H] and used extensively in the program initiated by Abbas et al. [ACH] to prove the strong Weinstein conjecture in dimension three. However, due to the lack of a compactness result of the moduli space of H-holomorphic curves, Abbas and his coworkers were only able to prove the strong Weinstein conjecture in the planar case, i.e. when the leaves of the holomorphic open book decomposition have zero genus. In this talk we describe a compactification of the moduli space of finite energy H-holomorphic curves under certain conditions. This is joint work with Urs Fuchs.
[H] H. Hofer, Holomorphic curves and real three-dimensional dynamics, Geom. Funct. Anal. Special Volume 2000, Part II (2000) 674 – 704
[ACH] C. Abbas, K. Cieliebak, H. Hofer, The Weinstein conjecture for planar contact structures in dimension three, Comment. Math. Helv. 80 (2005) 771 – 793

Mittwoch, den 6. Dezember 2017 um 11.30-13.00 Uhr, in Mathematikon, INF 205, SR 6 Mittwoch, den 6. Dezember 2017 at 11.30-13.00, in Mathematikon, INF 205, SR 6

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers