Knotting of Algebraic Curves in CP2
Abstract
Description
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.
9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the Intro
9 pages, 4 figures. Revision: an Appendix with a Figure is added; a minor correction in the Intro