Knotting of Algebraic Curves in CP2

Details Knotting of Algebraic Curves in CP2 Knotting of Algebraic Curves in CP2

1999-07-16

arxiv.org/abs/math/9907108v3

Mathematics

Geometric Topology

9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the Intro

Scientific paper

I construct "fake algebraic curves" in $Cp^2$. More precisely, for any k>2, I construct infinitely many pairwise smoothly non-isotopic (and moreover not ambient diffeomorphic) smooth surfaces $F\subset Cp^2$ homeomorphic to a non-singular algebraic curve of degree 2k, realizing the same homology class as such a curve and having abelian fundamental group of the complement $Cp^2-F$. This gives an answer to Problem 4.110 of Kirby's list.

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