Representing de Rham cohomology classes on an open Riemann surface by holomorphic forms
Date
2017
Authors
Alarcón, A.
Lárusson, F.
Editors
Advisors
Journal Title
Journal ISSN
Volume Title
Type:
Journal article
Citation
International Journal of Mathematics, 2017; 28(9):1740004-1-1740004-12
Statement of Responsibility
Antonio Alarcón, Finnur Lárusson
Conference Name
Abstract
Let X be a connected open Riemann surface. Let Y be an Oka domain in the smooth locus of an analytic subvariety of Cn, n ≥ 1, such that the convex hull of Y is all of Cn. Let O∗(X, Y ) be the space of nondegenerate holomorphic maps X → Y. Take a holomorphic 1-form θ on X, not identically zero, and let π : O∗(X, Y ) → H1(X, Cn) send a map g to the cohomology class of gθ. Our main theorem states that π is a Serre fibration. This result subsumes the 1971 theorem of Kusunoki and Sainouchi that both the periods and the divisor of a holomorphic form on X can be prescribed arbitrarily. It also subsumes two parametric h-principles in minimal surface theory proved by Forstneriˇc and L´arusson in 2016.
School/Discipline
Dissertation Note
Provenance
Description
Access Status
Rights
© World Scientific Publishing Company