Rational homology of spaces of complex monic polynomials with multiple roots

2001/11/14 by Dmitry N. Kozlov
Mathematics · #math.CO #math.AT #msc:32S20 #msc:05E15 #msc:32S60 #msc:58K15

paper · pdf

published as Mathematika 49 (2002), no. 1-2, 77--91 (2004).

arxiv created 2001/11/14 · arxiv updated 2009/11/30

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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