Rational homotopy type of the moduli of representations with Borel mold
type: Item
instance of: scholarly article
title: Rational homotopy type of the moduli of representations with Borel mold
zbMATH Open document ID: 1253.55009
author: Kazunori Nakamoto
author: Takeshi Torii
published in: Forum Mathematicum
publication date: 2012-06-11T00:00:00Z
Mathematics Subject Classification ID: 55P62
Mathematics Subject Classification ID: 14C30
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14D22
zbMATH DE Number: 6044926
zbMATH Keywords: rational homotopy type
zbMATH Keywords: moduli space of representations
zbMATH Keywords: representations with Borel mold
MaRDI profile type: Publication
full work available at URL: form.2011.071
OpenAlex ID: W2332681792
cites work: On loop spaces of configuration spaces
cites work: Théorie de Hodge. II. (Hodge theory. II)
cites work: Théorie de Hodge. III
cites work: Representation varieties and character varieties
cites work: Topology of the moduli of representations with Borel mold
cites work: Infinitesimal computations in topology
DOI: 10.1515/FORM.2011.071
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review text: The authors investigate representations of free algebras or free monoids. Let \(\text{Rep}_n(m)_B\) be the moduli space of representations with Borel mold of degree \(m\) for the free monoid with \(n\) generators, and let \(B_n(m)_B\) be a subscheme of \(\text{Rep}_n(m)_B\) which consists of the representations with Borel mold in upper triangular matrices. The associated character variety of \(\text{Rep}_n(m)_B\) is denoted \(\text{Ch}_n(m)_B\).NEWLINENEWLINE The first main theorem in this note is: If \(K\) is one of the three complex algebraic varieties considered above then \(K\) is rationally homotopy equivalent to the product of the configuration space of \(n\) distinct points in \(\mathbb{C}^n\) and the product of \((n-1)\) copies of the projective space \(\mathbb{C} P^{m-2}\). The second main theorem describes the Sullivan minimal model of \(K\) with mixed Hodge structure as formerly studied by Morgan.
reviewed by: Jean-Claude Thomas
description: scientific article; zbMATH DE number 6044926