Higgs bundles and teichmuller space

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August undefined, 2024

Web8 de mar. de 2024 · These different perspectives lead to interesting generalizations known as higher Teichmuller spaces. Higgs bundles on Riemann surfaces are holomorphic bundles with an auxiliary feature known as the Higgs field. With roots in physical and mathematical gauge theory they have moduli spaces with rich algebraic and geometric … Web00:00 Abstract I will review the basic concepts of Higgs bundles and the moduli space of Higgs bundles, and then focus the non-Abelian Hodge correspondence: relation between the moduli space of Higgs bundles with harmonic maps and the character variety.

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WebHiggs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize a result of Hitchin, identifying … Web2.2 The Higgs bundle moduli space and deformation theory. In general, these stability notions involve the interaction of the Higgs field with certain parabolic reductions of … great crested grebe

Hitchin’s Projectively Flat Connection and the Moduli Space of …

Web3. S.!Bradlow,!B.!Goldman,!O.!GarcíaEPrada!and!A.!Wienhard,!!Backround!notes!prepared! … Web2 de mar. de 2024 · These results are proven in two steps, first we use Higgs bundles to give a non-mapping class group equivariant parameterization, then we prove an analogue of Labourie's conjecture for maximal PSp ... Web2.1.3 Quadratic diﬀerentials and Teichmuller¨ maps. . . . . . . 9 ... • M(S,r) = the moduli space of polystable Higgs bundles of rank ron S (Section 3.2.1). 6 Georgios D. Daskalopoulos and Richard A. Wentworth 2 Teichmull¨ er Space and Extremal Maps • 2.1 The Teichmull¨ er Theorems great crested grebe breeding season

Higher Teichmüller spaces and Higgs bundles

Webfolds. In Chapter 7 we geometrically quantize the Higgs line bundle moduli space, and investigate the di culties of generalising the techniques used to the higher rank spaces. In particular we construct a projectively at Hitchin connection on the bundle of quantum spaces over Teichmuller space. As far as the author is aware, this is an original ... WebTeichmuller space. In general, the bre of M( ;RH4) over c 2T g is isomorphic to the nilpotent cone in H(c;G), or to be precise, the open subset of this which corresponds to indecomposable Higgs bundles. By Hausel’s Theorem [18] the nilpotent cone is a union of the unstable manifolds of the downwards gradient ow for the Higgs bundle energy (which great-crested grebeWeb7 de fev. de 2024 · Date/Time:17 Apr 2024 15:00 Venue: S17 #05-11 SR5 Speaker: Oscar Garcia-Prada, ICMAT, Madrid Higgs bundles and higher Teichmüller spaces Some... great crested grebe bird

"Web14 de dez. de 2024 · We introduce the notions of deformation Higgs bundle and Riemann-Finsler metric on the moduli space of polarized varieties. We also use the Higgs-de … " - Higgs bundles and teichmuller space

Higgs bundles and teichmuller space

WebSearch results for citedby:recid:1675144. Number of results: 7 ≪ < page 1 of 1 > ≫ Brief list Raw JSON Webof the orbifold fundamental group. Moreover, the Teichmuller space in the orbifold case was studied in [38], as well as the topology of the moduli space of Higgs bundles in the orbifold situation for rank 2 bundles. Under the correspondence between parabolic Higgs bundles and Higgs V-bundles, we map

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WebTEICHMULLER SPACES ¨ STEVEN BRADLOW ... Moduli spaces of Higgs bundles 38 6.1. Stability conditions and moduli spaces 38 6.2. Local structure of the moduli spaces 39 6.3. The Hitchin map 40 6.4. The Hitchin–Kobayashi correspondence 41 7. The generalized Cayley correspondence 42

Web14 de nov. de 1995 · and para b olic Higgs bundles, F uc hsian represen tations of n-punctured Riemann surfaces are in one-one correspondence with parab olic Higgs … Web25 de jan. de 2024 · This paper is a survey on the role of Higgs bundle theory in the study of higher Teichmüller spaces. Recall that the Teichmüller space of a compact surface …

Web15 de dez. de 2024 · Show abstract Parabolic Higgs bundles and Teichmüller spaces for punctured surfaces Article Full-text available Apr 1997 Indranil Biswas Pablo Arés-Gastesi Suresh Govindarajan View Show... Webto PSL(2;R) is called the Teichmuller space of . ... with a lattice in a simple noncompact connected Lie group Hwithout center. Higgs bundles and representations of complex hyperbolic lattices 3 and not locally isomorphic to PSL(2;R) are uniquely determined by . This is the content of Mostow strong rigidity theorem ([38,40]).

WebThe higher Teichmuller space is originally de ned by Hitchin. Therefore this space is often called the Hitchin component. He used the Higgs bundle to study the representation space and showed the following theorem.. Theorem(Hitchin ’92)..Hit n(S) is homeomorphic to R(2g 2)(n 2 1). However, in his article, he said

Web11 de jan. de 2024 · This course is an introduction to the moduli space of Higgs bundles, introduced by Hitchin in 1987 and sometimes called the Hitchin moduli space. It is a … great crested geckohttp://geomgrav.fi.ut.ee/inspire/search.php?q=citedby:recid:1675144 great crested grebe nesthttp://geomgrav.fi.ut.ee/inspire/search.php?q=citedby:recid:1809798 great crested grebe rspbWeb14 de nov. de 1995 · In this paper we study the relation between parabolic Higgs bundles and irreducible representations of the fundamental group of punctured Riemann surfaces established by Simpson. We generalize... great crested grebes crossword clueWeb25 de jan. de 2024 · This paper is a survey on the role of Higgs bundle theory in the study of higher Teichmuller spaces. Recall that the Teichmuller space of a compact surface … great crested grebe nativeWebThe notion of a Higgs bundle was introduced by Hitchin in [14] and has been widely studied from di erent points of view. The moduli space of Higgs bundles includes Teichmuller space when we consider discrete and faithful representations to SL(2;R) (see [10], [32]) and further generalizes to the concept of higher Teichmuller great crested flycatcher picturesWeb5 de abr. de 2014 · Together, these two results allow the character variety for representations of the fundamental group of a Riemann surface in a Lie group G to be identified with a moduli space of holomorphic objects, known as G -Higgs bundles. great crested grebe call