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Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces

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cshays2006.pdf (618.37 KB)

Date

2006

Authors

Hays, Christopher

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University of Waterloo

Abstract

<html> <head> <meta http-equiv="Content-Type" content="text/html;charset=iso-8859-1"> </head> Let &Sigma;<em><sub>g</sub></em> be a closed Riemann surface of genus <em>g</em>. Generalizing Ivan Smith's construction, for each <em>g</em> &ge; 1 and <em>h</em> &ge; 0 we construct an infinite set of infinite families of homotopic but pairwise non-isotopic symplectic surfaces inside the product symplectic manifold &Sigma;<em><sub>g</sub></em> ×&Sigma;<em><sub>h</sub></em>. In particular, we achieve all positive genera from these families, providing first examples of infinite families of homotopic but pairwise non-isotopic symplectic surfaces of even genera inside &Sigma;<em><sub>g</sub></em> ×&Sigma;<em><sub>h</sub></em>.

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Keywords

Mathematics, Symplectic Manifolds, Isotopy Problem, Branched Covers

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http://hdl.handle.net/10012/2917

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Pure Mathematics