Room 515, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館515研討室+ Zoom)
h-Principles in Smooth and Complex Geometry
Guillermo Sánchez Arellano (Universidad Complutense de Madrid)
Abstract: The goal of the -principle theory is to understand when a geometric problem is governed by the laws of differential topology. When topology (more flexible) overrides geometry (more rigid), we say that the -principle holds in that context. The -principle theory has been especially fruitful in scenarios that exhibit both rigid and flexible properties, such as in the symplectic and contact settings.
The identity principle and the resulting lack of partitions of unity endow complex geometry with great rigidity. However, there is a class of complex manifolds, Stein manifolds, in which the Oka principle, a type of -principle for holomorphic functions, holds. The flexible properties of Stein manifolds have been exploited by . Forstneric and . Slapar to establish -principles for holomorphic immersions and submersions, and by . Forstnerič for complex contact forms.
In this talk, we will review some of the most recent -principle results in the smooth category, and explore how to abstract Forstneric and Slapar's techniques to obtain more general holomorphic -principles in Stein manifolds.
Meeting ID: 819 6635 8853
Passcode: 604161
Organizers: River Chiang (NCKU) & Chung-Jun Tsai (NTU)
