科研之友
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摘要
We develop obstructions to a knot K subset of S-3 bounding a smooth punctured Klein bottle in B-4. The simplest of these is based on the linking form of the 2-fold branched cover of S-3 branched over K. Stronger obstructions are based on the Ozsvath-Szabo correction term in Heegaard-Floer homology, along with the G-signature theorem and the Guillou-Marin generalization of Rokhlin's theorem. We also apply Casson-Gordon theory to show that for every n > 1 there exists a knot that does not bound a topologically embedded ribbon nonorientable surface F in B-4 with first Betti number beta(1)(F) < n.
- 出版日期2011-12
