The Cohomological Genus and Symplectic Genus for 4-Manifolds of Rational or Ruled Types
Keyword(s):
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.
1980 ◽
Vol 3
(3)
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pp. 1049-1053
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2014 ◽
Vol 229
(5)
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pp. 957-964
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Keyword(s):
2008 ◽
Vol 2008
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pp. 1-19
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Keyword(s):
1998 ◽
Vol 88
(1-2)
◽
pp. 3-25
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