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Non-Isotopic Symplectic Surfaces in Products of Riemann Surfaces

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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>.

Identiferoai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/2917
Date January 2006
CreatorsHays, Christopher
PublisherUniversity of Waterloo
Source SetsUniversity of Waterloo Electronic Theses Repository
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatapplication/pdf, 633210 bytes, application/pdf
RightsCopyright: 2006, Hays, Christopher. All rights reserved.

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