The Cohomological Genus and Symplectic Genus for 4-Manifolds of Rational or Ruled Types

Mathematics

Chung-I Ho¹  Bo Dai² 

[1] Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan;Laboratory of Mathematics and Its Applications, School of Mathematical Sciences, Peking University, Beijing 100871, China;

关键词: minimal genus;    symplectic genus;    rational surface;    ruled surface;   

DOI  :  10.3390/math9131563

来源: DOAJ

【 摘 要 】

An important problem in low dimensional topology is to understand the properties of embedded or immersed surfaces in 4-dimensional manifolds. In this article, we estimate the lower genus bound of closed, connected, smoothly embedded, oriented surfaces in a smooth, closed, connected, oriented 4-manifold with the cohomology algebra of a rational or ruled surface. Our genus bound depends only on the cohomology algebra rather than on the geometric structure of the 4-manifold. It provides evidence for the genus minimizing property of rational and ruled surfaces.

【 授权许可】

Unknown