"Teichmuller theory"의 두 판 사이의 차이

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==introduction==
  
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==review of hyperbolic geometry==
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*  horocycle
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** http://en.wikipedia.org/wiki/Horocycle
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** http://web1.kcn.jp/hp28ah77/us15_horo.htm
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* exponentiated hyperbolic distances between horocycles drawn around vertices of a polygon with geodesic sides and cusps at the vertices
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* lamination
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* shear coordinates
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* lambda length
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* http://moniker.name/worldmaking/?p=744
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* http://orion.math.iastate.edu/dept/thesisarchive/MSCC/OLearyMSCCSS06.pdf
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* \def
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* An ideal triangle in (S,M) is a triangle with vertices at M, whose sides are geodesics.
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* \def
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* A horocycle at marked point p is a set of points "equidistant" to p. In lift to H^2, looks like circle tangent to boundary at p.
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==Teichmuller space of a marked surface==
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Given marked surface (S,M) , the Teichmuller space T(S,M) is the space of metrics on (S,M) such that
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* are hyperbolic  (constant curvature -1)
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* have geodesic boundary at boundary of S
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* local neighborhood of point on boundary S can be mapped isometrically to neighborhood of a point here on one side of geodesic
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* have cusps at points in M
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Considered up to diffeomorphism homotopic to identity.
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Facts
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(1) T(S,M) contractible
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(2) T(S,M) is manifold of dimension 6g-6+2p+3b+c where g = genus, p=# of puncture, b = # boundary component, c=# of marked points on boundary
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==related items==
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* [[Moduli space of local systems and higher Teichmuller theory]]
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==expositions==
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* Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos, On Grothendieck's construction of Teichmüller space, http://arxiv.org/abs/1603.02229v1
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* Matheus, Carlos. “Lecture Notes on the Dynamics of the Weil-Petersson Flow.” arXiv:1601.00690 [math], January 4, 2016. http://arxiv.org/abs/1601.00690.
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* Papadopoulos, Athanase, Vincent Alberge, and Weixu Su. “A Commentary on Teichm"uller’s Paper ‘Extremale Quasikonforme Abbildungen Und Quadratische Differentiale.’” arXiv:1511.01313 [math], November 4, 2015. http://arxiv.org/abs/1511.01313.
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* [http://www.ems-ph.org/books/055/9783037190296_introduction.pdf Introduction to Teichmüller theory, old and new], Athanase Papadopoulos
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==articles==
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* Leonid Chekhov, Marta Mazzocco, Colliding holes in Riemann surfaces and quantum cluster algebras, arXiv:1509.07044 [math-ph], September 23 2015, http://arxiv.org/abs/1509.07044
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* Lien-Yung Kao, Pressure type metrics on spaces of metric graphs, arXiv:1604.03173 [math.DS], April 11 2016, http://arxiv.org/abs/1604.03173
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* Babak Modami, Asymptotics of a class of Weil-Petersson geodesics and divergence of Weil-Petersson geodesics, Algebr. Geom. Topol. 16 (2016) no.1, pp. 267-323, http://arxiv.org/abs/1401.3234v4
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* Antonakoudis, Stergios M. “The Complex Geometry of Teichm"uller Spaces and Bounded Symmetric Domains.” arXiv:1510.07340 [math], October 25, 2015. http://arxiv.org/abs/1510.07340.
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* Penner, R. C., and Anton M. Zeitlin. “Decorated Super-Teichm"uller Space.” arXiv:1509.06302 [hep-Th, Physics:math-Ph], September 21, 2015. http://arxiv.org/abs/1509.06302.
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[[분류:개인노트]]
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[[분류:cluster algebra]]
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[[분류:math and physics]]
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[[분류:math]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q2400539 Q2400539]
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===Spacy 패턴 목록===
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* [{'LOWER': 'teichmüller'}, {'LEMMA': 'space'}]

2021년 2월 17일 (수) 02:32 기준 최신판

introduction

review of hyperbolic geometry



Teichmuller space of a marked surface

Given marked surface (S,M) , the Teichmuller space T(S,M) is the space of metrics on (S,M) such that

  • are hyperbolic (constant curvature -1)
  • have geodesic boundary at boundary of S
  • local neighborhood of point on boundary S can be mapped isometrically to neighborhood of a point here on one side of geodesic
  • have cusps at points in M

Considered up to diffeomorphism homotopic to identity.

Facts

(1) T(S,M) contractible

(2) T(S,M) is manifold of dimension 6g-6+2p+3b+c where g = genus, p=# of puncture, b = # boundary component, c=# of marked points on boundary





related items



expositions

articles

  • Leonid Chekhov, Marta Mazzocco, Colliding holes in Riemann surfaces and quantum cluster algebras, arXiv:1509.07044 [math-ph], September 23 2015, http://arxiv.org/abs/1509.07044
  • Lien-Yung Kao, Pressure type metrics on spaces of metric graphs, arXiv:1604.03173 [math.DS], April 11 2016, http://arxiv.org/abs/1604.03173
  • Babak Modami, Asymptotics of a class of Weil-Petersson geodesics and divergence of Weil-Petersson geodesics, Algebr. Geom. Topol. 16 (2016) no.1, pp. 267-323, http://arxiv.org/abs/1401.3234v4
  • Antonakoudis, Stergios M. “The Complex Geometry of Teichm"uller Spaces and Bounded Symmetric Domains.” arXiv:1510.07340 [math], October 25, 2015. http://arxiv.org/abs/1510.07340.
  • Penner, R. C., and Anton M. Zeitlin. “Decorated Super-Teichm"uller Space.” arXiv:1509.06302 [hep-Th, Physics:math-Ph], September 21, 2015. http://arxiv.org/abs/1509.06302.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'teichmüller'}, {'LEMMA': 'space'}]
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