"Teichmuller theory"의 두 판 사이의 차이
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imported>Pythagoras0 (section 'articles' updated) |
imported>Pythagoras0 (section 'expositions' updated) |
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| 57번째 줄: | 57번째 줄: | ||
==expositions== | ==expositions== | ||
| + | * Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos, On Grothendieck's construction of Teichmüller space, http://arxiv.org/abs/1603.02229v1 | ||
* 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. | * 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. | ||
* 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. | * 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. | ||
2016년 3월 8일 (화) 01:43 판
introduction
review of hyperbolic geometry
- horocycle
- exponentiated hyperbolic distances between horocycles drawn around vertices of a polygon with geodesic sides and cusps at the vertices
- lamination
- shear coordinates
- lambda length
- http://moniker.name/worldmaking/?p=744
- http://orion.math.iastate.edu/dept/thesisarchive/MSCC/OLearyMSCCSS06.pdf
- \def
- An ideal triangle in (S,M) is a triangle with vertices at M, whose sides are geodesics.
- \def
- 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.
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
expositions
- Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos, On Grothendieck's construction of Teichmüller space, http://arxiv.org/abs/1603.02229v1
- 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.
- 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.
- Introduction to Teichmüller theory, old and new, Athanase Papadopoulos
articles
- 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.