Topology of spaces of hyperbolic polynomials and combinatorics of resonances

Details Topology of spaces of hyperbolic polynomials and combinatorics of resonances Topology of spaces of hyperbolic polynomials and combinatorics of resonances

2001-11-14

arxiv.org/abs/math/0111166v1

Israel J. Math. 132 (2002), 189--206.

Mathematics

Combinatorics

Scientific paper

In this paper we study the topology of the strata, indexed by number partitions $\lambda$, in the natural stratification of the space of monic hyperbolic polynomials of degree $n$. We prove stabilization theorems for removing an independent block or an independent relation in $\lambda$. We also prove contractibility of the one-point compactifications of the strata indexed by a large class of number partitions, including $\lambda=(k^m,1^r)$, for $m\geq 2$. Furthermore, we study the maps between the homology groups of the strata, induced by imposing additional relations (resonances) on the number partition $\lambda$, or by merging some of the blocks of $\lambda$.

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