| Language |
English
|
| From |
2009/07/29 14:00
|
| To |
2009/07/29 15:00
|
| Place | Room 305, Building No.3, Faculty of Science, Kyoto University |
| Seminar Name | Seminar on Hyperplane Arrangement |
| Title |
Discrete Morse Theory for Arrangements of Hyperplanes |
| Field |
Geometry
|
| Speakers | Emanuele Delucchi |
| Affiliation | State University of New York |
| Note | The topological space obtained by removing a set of hyperplanes
from a finite dimensional complex vector space has many interesting
features. For instance, every such space is {\em minimal} - in the sense
that it has the homotopy type of a CW complex with as many cells in every
dimension as there are generators of the corresponding homology group. The
central question about complements of hyperplane arrangements is to study
to what extent the topology of the complement is determined by the
combinatorics of the pattern of intersections of the hyperplanes.
The goal of the talk is to introduce some basics of the theory of
hyperplane arrangements and to show that the above-mentioned minimality
property can be deduced from purely combinatorial considerations (at least
in the case where the hyperplanes are defined by real linear forms). The
techniques and ideas used thereby bear independent and general interest. |