Harmonic mappings of Kähler manifolds to locally symmetric spaces

Carlson, James A.; Toledo, Domingo

doi:10.1007/bf02698844

Cited by 134 publications

(151 citation statements)

References 32 publications

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“…For instance, using the above mentioned techniques of classifying spaces and harmonic maps, plus some Lie theoretic arguments, Carlson and Toledo [75], while giving alternative proofs of the results of Siu, prove:…”

Section: Concluding This Section It Is Clear How the Results Of Siu mentioning

confidence: 99%

Topological methods in moduli theory

Catanese

2015

Bull. Math. Sci.

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One of the main themes of this long article is the study of projective varieties which are K(H,1)'s, i.e. classifying spaces BH for some discrete group H. After recalling the basic properties of such classifying spaces, an important class of such varieties is introduced, the one of Bagnera-de Franchis varieties, the quotients of an Abelian variety by the free action of a cyclic group. Moduli spaces of Abelian varieties and of algebraic curves enter into the picture as examples of rational K(H,1)'s, through Teichmüller theory. The main trhust of the paper is to show how in the case of K(H,1)'s the study of moduli spaces and deformation classes can be achieved through by now classical results concerning regularity of classifying maps. The Inoue type varieties of Bauer and Catanese are introduced and studied as a key example, and new results are shown. Motivated from this study, the moduli spaces of algebraic varieties, and especially of algebraic curves with a group of automorphisms of a given topological type are studied in detail, following new results by the author, Michael Lönne and Fabio Perroni. Finally, the action of the absolute Galois group on the moduli spaces of such K(H,1) varieties is studied. In the case of surfaces isogenous to a product, it is shown how this yields a faifhtul action on the set of connected components of the moduli space: for each Galois automorphism of order different from 2 there is an Communicated by Efim Zelmanov.The present work took place in the realm of the DFG Forschergruppe 790 "Classification of algebraic surfaces and compact complex manifolds". Part of the article was written when the author was visiting KIAS, Seoul, as KIAS research scholar.

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Section: Concluding This Section It Is Clear How the Results Of Siu mentioning

confidence: 99%

Topological methods in moduli theory

Catanese

2015

Bull. Math. Sci.

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“…In this section, we exploit the full strength of Theorem 2.1 to prove a result that was first obtained by J. A. Carlson and D. Toledo in [6] in the case Γ is cocompact and ρ(Γ) is discrete in PU(n, 1) or in a more general target Lie group G. Their proof relies on a careful study of maximal abelian subalgebras of the complexification of the Lie algebra of G. In our setting, the simple form of the curvature tensor of (H n C , g n ) allows a more elementary proof that we give for completeness. Before proving this proposition, we introduce some notations that will be needed in the proof and later on in the paper.…”

Section: Holomorphicity Of "High" Rank Harmonic Mapsmentioning

confidence: 96%

Harmonic maps and representations of non-uniform lattices of {\rm PU}(m,1)

Koziarz¹,

Maubon²

2008

Ann. inst. Fourier

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“…Proof. It is clear that (3) implies (2). The converse is the celebrated Seifert fiber space conjecture, the final cases of which were resolved by Casson-Jungreis [3] and by Gabai [6].…”

Section: Three-manifold Groups Presentable By Productsmentioning

confidence: 97%

“…The study of non-zero degree maps between closed, oriented manifolds has become very active over the last few decades [2,7,14]. The existence of a non-zero degree map, M −→ N, defines a transitive relation on the set of homotopy types of closed, oriented manifolds.…”

Section: Introductionmentioning

confidence: 99%

On three-manifolds dominated by circle bundles

Kotschick

Neofytidis

2012

Math. Z.

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We determine which three-manifolds are dominated by products. The result is that a closed, oriented, connected three-manifold is dominated by a product if and only if it is finitely covered either by a product or by a connected sum of copies of S 2 × S 1 . This characterization can also be formulated in terms of Thurston geometries, or in terms of purely algebraic properties of the fundamental group. We also determine which three-manifolds are dominated by non-trivial circle bundles, and which three-manifold groups are presentable by products.

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Harmonic mappings of Kähler manifolds to locally symmetric spaces

Cited by 134 publications

References 32 publications

Topological methods in moduli theory

Topological methods in moduli theory

Harmonic maps and representations of non-uniform lattices of {\rm PU}(m,1)

On three-manifolds dominated by circle bundles

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