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


Tursday, 1 March, at 15:00 hrs.


Professor Yuri Muranov
(Vitebsk State University, Belarus)


"Surgery on manifolds with filtration"

Abstract: A  fundamental problem  of geometric topology is to describe
all possible manifolds which are homotopy (simple homotopy)
equivalent to a given manifold X.
The set of equivalence classes  form a
  structure set S(X) which fits into the surgery exact
sequence.  To describe the set S(X) we must know the set
of normal invariants  [x,G/TOP], the surgery obstruction groups
L_*(\pi), and  the  assembly map $[X,G/TOP]\to L_*(\pi)$.
The image of assembly map consists of elements that
can be realized by normal maps of closed manifolds.
In this talk, we  describe relations between assembly maps,
  manifolds with filtration, Browder-Quinn surgery obstruction groups
for stratified manifolds,  Browder-Livesay
invariants,  and surgery spectral sequence. In particular,  we give
geometrical desription of forbidden invariants in closed  manifold
  surgery problem and consider several examples.


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