Bundles with totally disconnected structure group

Wood, John W.

doi:10.1007/bf02566843

Cited by 164 publications

(116 citation statements)

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“…The proof is based on the Milnor-Wood inequality [97] and Goldman's theorem [59] and there is a terse exposition of these results (the proof of Goldman's theorem being essentially Matsumoto's [80]). These are best read from the original sources.…”

Section: N2 Fuchsian Holonomymentioning

confidence: 99%

Notes on a paper of Mess

et al. 2007

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Section: N2 Fuchsian Holonomymentioning

confidence: 99%

Notes on a paper of Mess

et al. 2007

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“…(Milnor [66] and Wood [81]). Call a representation maximal if equality holds in in (5.3.1), that is, Euler(ρ) = ±χ(Σ):…”

Section: The Euler Class and Components Of Hom(π Psl(2 R))mentioning

confidence: 99%

Higgs Bundles and Geometric Structures on Surfaces

Goldman¹

2010

The Many Facets of Geometry

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“…There are several ways to define it; for instance, a representation 2 R g defines a circle bundle on † g , which has a Z-valued characteristic class, the Euler class. We will review this Euler class and its properties in detail in Section 2.3, and also refer to Milnor [30], Wood [44], Ghys [14], Matsumoto [28], Goldman [20] and Calegari [6] for a deep understanding of this class.…”

Section: Introductionmentioning

confidence: 99%

Connected components of the compactification of representation spaces of surface groups

Wolff

2011

Geom. Topol.

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The Thurston compactification of Teichmüller spaces has been generalised to many different representation spaces by Morgan, Shalen, Bestvina, Paulin, Parreau and others. In the simplest case of representations of fundamental groups of closed hyperbolic surfaces in PSL.2; R/, we prove that this compactification behaves very badly: the nice behaviour of the Thurston compactification of the Teichmüller space contrasts with wild phenomena happening on the boundary of the other connected components of these representation spaces. We prove that it is more natural to consider a refinement of this compactification, which remembers the orientation of the hyperbolic plane. The ideal points of this compactification are oriented R-trees, ie, R-trees equipped with a planar structure. 53C23; 20H10, 32G15

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Bundles with totally disconnected structure group

Cited by 164 publications

References 3 publications

Notes on a paper of Mess

Notes on a paper of Mess

Higgs Bundles and Geometric Structures on Surfaces

Connected components of the compactification of representation spaces of surface groups

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