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

    Extended complexity of 3-manifolds

    Sergei Matveev
    ( Click here for pdf version )

    Any compact 3-manifold $M$ has a complexity $c(M)$, which is a nonnegative integer number and which is defined as the number of true vertices of a minimal almost simple spine $P$ of $M$. The complexity has many good properties. In particular, it behave well with respect to cutting $M$ along surfaces. Namely, if $M_F$ is obtained from $M$ by cutting along an incompressible surface $F\subset M$, then $c(M_F)\leq c(M)$. However, this useful property has a shortcoming: the inequality is not strong. So we cannot use it for inductive proofs. We improve that by defining extended complexity $\bar c(M)$. It is not a number anymore, but a finite tuple of nonnegative integers. The tuples are considered in lexicographical ordering. We prove that if $F$ is essential, then $\bar c(M_F)< \bar c(M)$. We apply the extended complexity for proving the algorithmic classification theorem for Haken 3-manifolds.