"Teichmuller theory"의 두 판 사이의 차이
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encyclopedia==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| − | ==introduction | + | ==introduction== |
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| − | ==review of hyperbolic geometry | + | ==review of hyperbolic geometry== |
* horocycle<br> | * horocycle<br> | ||
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| − | ==Teichmuller space of a marked surface | + | ==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 | 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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| − | ==history | + | ==history== |
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| − | ==related items | + | ==related items== |
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| − | ==books | + | ==books== |
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* [http://www.ems-ph.org/books/055/9783037190296_introduction.pdf Introduction to Teichmüller theory, old and new], Athanase Papadopoulos | * [http://www.ems-ph.org/books/055/9783037190296_introduction.pdf Introduction to Teichmüller theory, old and new], Athanase Papadopoulos | ||
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2012년 10월 28일 (일) 15:55 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
history
encyclopedia==
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://eom.springer.de
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
expositions
- Introduction to Teichmüller theory, old and new, Athanase Papadopoulos
articles==
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links
- http://www.ams.org/mathscinet
- http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/
question and answers(Math Overflow)
- http://mathoverflow.net/search?q=
- http://math.stackexchange.com/search?q=
- http://physics.stackexchange.com/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links