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Topology of spaces of hyperbolic polynomials and combinatorics of resonances

Dmitry N. Kozlov
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Abstract

In this paper we study the topology of the strata, indexed by number partitions $λ$, 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 $λ$. We also prove contractibility of the one-point compactifications of the strata indexed by a large class of number partitions, including $λ=(k^m,1^r)$, 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 $λ$, or by merging some of the blocks of $λ$.

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Dmitry N. Kozlov. 2001-11-14. Topology of spaces of hyperbolic polynomials and combinatorics of resonances. https://arxiv.org/abs/math/0111166

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