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Type: Artigo de periódico
Title: On the geometry of moduli spaces of anti-self-dual connections
Author: Ballico, E
Eyral, C
Gasparim, E
Abstract: Consider a simply connected, smooth, projective, complex surface X. Let M-k(f) (X) be the moduli space of framed irreducible anti-self-dual connections on a principal SU(2)-bundle over X with second Chern class k > 0, and let C-k(f) (X) be the corresponding space of all framed connections, modulo gauge equivalence. A famous conjecture by M. Atiyah and J. Jones says that the inclusion map M-k(f) (X) -> C-k(f) (X) induces isomorphisms in homology and homotopy through a range that grows with k. In this paper, we focus on the fundamental group, pi(1). When this group is finite or polycyclic-by-finite, we prove that if the pi(1)-part of the conjecture holds for a surface X, Keywords: then it also holds for the surface obtained by blowing up X at n points. As a corollary. Anti-self-dual connections we get that the pi(1)-part of the conjecture is true for any surface obtained by blowing up n times the complex projective plane at arbitrary points. Moreover, for such a surface, the fundamental group pi(1)(M-k(f)(X)) is either trivial or isomorphic to Z(2). (C) 2011 Elsevier B.V. All rights reserved.
Subject: Anti-self-dual connections
Stable holomorphic bundles
Atiyah-Jones conjecture for the fundamental group
Rectified homotopy depth
Country: Holanda
Editor: Elsevier Science Bv
Citation: Topology And Its Applications. Elsevier Science Bv, v. 159, n. 3, n. 633, n. 645, 2012.
Rights: fechado
Identifier DOI: 10.1016/j.topol.2011.10.011
Date Issue: 2012
Appears in Collections:Unicamp - Artigos e Outros Documentos

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