Homepage
Organizing Cmte.
Advisory Committee
Plenary speakers
Special Sessions
  • knot theory and quantum topology
  • 3-manifolds
  • 4-manifolds
  • Geometric group theory and related topics
  • Fixed point theory
    Abstracts (pdf)
    Schedule
    Accommodation
    Transportation
    Registration Form
    Confirmation
    List of Participants
    Passport and Visa
    Useful Links
  • Map of China
  • ICM 2002
  • About Xi'an
  • Qujiang Hotel

    Knotting of Curves in Complex Algebraic Surfaces

    Sergey Finashin
    ( Click here for pdf version )

    {\bf Theorem.} For any $d>4$ there exists an infinite family of smooth surfaces, $F_i$, in $CP^2$ which are homeomorphic to an algebraic curve, $A$, of degree $d$, realize the same homology class as $A$ and have the same as $A$ (i.e., abelian) fundamental group of the complement, $\pi_1(CP^2-F_i)$, but with the pairs $(CP^2,F_i)$ pairwise smoothly non-equivalent.

    Surfaces $F_i$ are obtained from $A$ by an annulus rim surgery. This surgery construction is a modification of the rim surgery used by Fintushel and Stern for similar knotting in the case of trivial fundamental group of the complement.

    The annulus rim surgery can be also used for knottings of curves in any complex algebraic surface provided the curves admit certain degenerations.