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Tuesday Seminar on Topology
Seminar information archive ～09/10｜Next seminar｜Future seminars 09/11～
| Date, time & place | Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya |
2011/10/25
16:30-18:00 Room #056 (Graduate School of Math. Sci. Bldg.)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
Andrei Pajitnov (Univ. de Nantes, Univ. of Tokyo)
Circle-valued Morse theory for complex hyperplane arrangements (ENGLISH)
[ Abstract ]
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.
We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.
We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.
This is a joint work with Toshitake Kohno.
Let A be a complex hyperplane arrangement
in an n-dimensional complex vector space V.
Denote by H the union of the hyperplanes
and by M the complement to H in V.
We develop the real-valued and circle-valued Morse
theory on M. We prove that if A is essential then
M has the homotopy type of a space
obtained from a finite n-dimensional
CW complex fibered over a circle,
by attaching several cells of dimension n.
We compute the Novikov homology of M and show
that its structure is similar to the
homology with generic local coefficients:
it vanishes for all dimensions except n.
This is a joint work with Toshitake Kohno.
