Modifying surfaces in 4-manifolds by twist spinning

Hee Jung Kim

doi:10.2140/gt.2006.10.27

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Modifying surfaces in 4-manifolds by twist spinning

Hee Jung Kim

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Abstract

In this paper, given a knot K, for any integer m we construct a new surface Sigma_K(m) from a smoothly embedded surface Sigma in a smooth 4-manifold X by performing a surgery on Sigma. This surgery is based on a modification of the `rim surgery' which was introduced by Fintushel and Stern, by doing additional twist spinning. We investigate the diffeomorphism type and the homeomorphism type of (X,Sigma) after the surgery. One of the main results is that for certain pairs (X,Sigma), the smooth type of Sigma_K(m) can be easily distinguished by the Alexander polynomial of the knot K and the homeomorphism type depends on the number of twist and the knot. In particular, we get new examples of knotted surfaces in CP^2, not isotopic to complex curves, but which are topologically unknotted.

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BibTeX RIS

Hee Jung Kim. 2009-03-03. Modifying surfaces in 4-manifolds by twist spinning. https://doi.org/10.2140/gt.2006.10.27

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