Mathematics Seminar at ICTP - THIS WEEK

[Math]

M A T H E M A T I C S  S E M I N A R S  2007


Thursday, 15 March, at 15:00 hrs.


Professor Yuri Muranov
(Vitebsk State University, Belarus)



"Classification of manifolds and splitting"

Abstract. Let $Y\subset X$ be a closed manifold pair. A simple homotopy
equivalence $f:M\to X$ of n-manifolds  splits
along the submanifold $Y$ if it is homotopy equivalent to a map which
is a simple homotopy equivalence on the transversal preimages of the
submanifold
and its compliment. In this situation the splitting obstruction
groups $LS_*$  are well defined and provide an evident obstruction to
existence a homeomorphism in the homotopy class of a simple homotopy
equivalence $f$.  The splitting obstruction groups
closely relates  to detecting what elements
of the Wall surgery obstruction group belong to the image of
the assembly map.  From the geometrical point of view the splitting
obstruction is an  obstruction to do
surgery inside the ambient manifold. We describe
relations betwwen surgery on manifold and the splitting problem
and give  a generalization of the splitting theory
  to the case of filtered manifolds.
We discuss the  applications of the splitting theory
to the classification of closed manifolds.


Venue: Seminar room (ICTP Main Building, first floor)