Homological action of the modular group on some cubic moduli spaces

dc.creatorGoldman, William M.
dc.creatorNeumann, Walter D.
dc.date2004-02-03
dc.date.accessioned2026-07-07T08:10:19Z
dc.date.available2026-07-07T08:10:19Z
dc.descriptionWe describe the action of the automorphism group of the complex cubic x^2+y^2+z^2-xyz-2 on the homology of its fibers. This action includes the action of the mapping class group of a punctured torus on the subvarieties of its SL(2,C) character variety given by fixing the trace of the peripheral element (so-called "relative character varieties"). This mapping class group is isomorphic to PGL(2,Z). We also describe the corresponding mapping class group action for the four-holed sphere and its relative SL(2,C) character varieties, which are fibers of deformations x^2+y^2+z^2-xyz-2-Px-Qy-Rz of the above cubic. The 2-congruence subgroup PGL(2,Z)_(2) still acts on these cubics and is the full automorphism group when P,Q,R are distinct.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/math/0402039
dc.identifierhttp://arxiv.org/abs/math/0402039
dc.identifierMath. Res. Lett. 12 (2005), no. 4, 575--591
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131791
dc.subjectGeometric Topology
dc.subject57M05, 30F60, 20H10
dc.titleHomological action of the modular group on some cubic moduli spaces
dc.typetext

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