Rational homology of spaces of complex monic polynomials with multiple roots

Dmitry N. Kozlov

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arXiv · math/0111167

Rational homology of spaces of complex monic polynomials with multiple roots

Dmitry N. Kozlov

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Abstract

We study rational homology groups of one-point compactifications of spaces of complex monic polynomials with multiple roots. These spaces are indexed by number partitions. A standard reformulation in terms of quotients of orbit arrangements reduces the problem to studying certain triangulated spaces $X_{λ,μ}$. We present a combinatorial description of the cell structure of $X_{λ,μ}$ using the language of marked forests. As applications we obtain a new proof of a theorem of Arnold and a counterexample to a conjecture of Sundaram and Welker, along with a few other smaller results.

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Dmitry N. Kozlov. 2001-11-14. Rational homology of spaces of complex monic polynomials with multiple roots. https://arxiv.org/abs/math/0111167

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