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

Bo Dai and Chung-I Ho
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Bo Dai: Laboratory of Mathematics and Its Applications, School of Mathematical Sciences, Peking University, Beijing 100871, China
Chung-I Ho: Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan

Mathematics, 2021, vol. 9, issue 13, 1-11

Abstract: 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.

Keywords: minimal genus; symplectic genus; rational surface; ruled surface (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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