Last updated November 25, 1998
The 7th Japan-Korea School of Knots and Links
February 15 - 19, 1999
Professor Akio Kawauchi will give a lecture at the school
as follows:
Title: On the fundamental class of an infinite cyclic covering
Abstract:
Infinite cyclic coverings of a compact connected oriented n-manifold M
are classified by the first cohomology classes of M, and hence are classified
by the leaf-submanifolds of M by Poincare duality, A standard example of
leaf-submanifold comes from a Seifert hypersurface for a manifold-link.
In this talk, we show how any two leaf-submanifolds belonging to the
same covering of M are connected via a sequence of embedded-handle surgeries
in M. In a process of the argument, we show that we can always construct a
connected leaf-submanifold from any given leaf-submanifold via a sequence of
1-embedded-handle surgeries in M when n>2 and the covering of M is connected.
An example on an immersed (n-1)-sphere in an n-manifold M with disconnected
boundary which is not homologous to any connected (n-1)-submanifold in M is
explained.
Information:
For more information, please send an e-mail to
nakanisi@math.kobe-u.ac.jp