Stratifications indexed by partitions and combinatorial models for homology
Royal Institute of Technology, Stockholm, Sweden
refreshments at 3:45pm
We shall consider several topological spaces equipped with stratifications
indexed by integer partitions. In each case we consider
the problem of studying homology groups of strata. We shall first describe how to
construct various models for computing these groups
and then present the following applications:
Determining the homology of resonance-free orbit arrangements (with the help of
general lexicographic shellability), thereby settling a
conjecture of Bjorner for this special case;
- A combinatorial reproof of Arnol'd theorem regarding the rational homology of the
space of monic complex polynomials with at least q
roots of multiplicity k;
- A counterexample to a conjecture by Sundaram and Welker;
- A computation of the homology groups of the space of hyperbolic polynomials with at
least q roots of multiplicity k.
Speaker's Contact Info: kozlov(at-sign)math.kth.se
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