ncku-talk2019-11-21

Geometry Seminar

DATE 2019-11-21　15:10-16:00

PLACE 數學館3F會議室

SPEAKER 李宜珍教授（香港中文大學數學系）

TITLE Holomorphic Curves and Seiberg-Witten Invariants for 4-Dimensional Cobordisms

ABSTRACT We will discuss a variant of Taubes’s Seiberg-Witten to Gromov theorem in the context of a 4-manifold with cylindrical ends, equipped with a nontrivial harmonic 2-form. This harmonic 2-form is allowed to be asymptotic to 0 on some (but not all) of its ends, and may have nondegenerate zeros along 1-submanifolds. Corollaries include various positivity results; some simple special cases of these constitute a key ingredient in Kutluhan-Lee-Taubes’s proof of HM = HF (Monopole Floer homology equals Heegaard Floer homology). The aforementioned general theorem is motivated by (potential) extensions of the HM = HF and Lee-Taubes’s HM = PFH (Periodic Floer homology) theorems.

Geometry Seminar

DATE	2019-11-21　15:10-16:00

PLACE	數學館3F會議室

SPEAKER	李宜珍教授（香港中文大學數學系）

TITLE	Holomorphic Curves and Seiberg-Witten Invariants for 4-Dimensional Cobordisms

ABSTRACT	We will discuss a variant of Taubes’s Seiberg-Witten to Gromov theorem in the context of a 4-manifold with cylindrical ends, equipped with a nontrivial harmonic 2-form. This harmonic 2-form is allowed to be asymptotic to 0 on some (but not all) of its ends, and may have nondegenerate zeros along 1-submanifolds. Corollaries include various positivity results; some simple special cases of these constitute a key ingredient in Kutluhan-Lee-Taubes’s proof of HM = HF (Monopole Floer homology equals Heegaard Floer homology). The aforementioned general theorem is motivated by (potential) extensions of the HM = HF and Lee-Taubes’s HM = PFH (Periodic Floer homology) theorems.