"Surfaces with punctures"의 두 판 사이의 차이
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<h5>tagged triangulation</h5> | <h5>tagged triangulation</h5> | ||
| − | * two tagged arcs are compatible if | + | * two tagged arcs are compatible if<br> (i) they do not cross<br> (ii) they are not isotopic except<br> |
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| + | tagged arc complex is the clique complex where simplices are collections of compatible tagged arcs | ||
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| + | \Theorem (Fomin, Shapiro, Thurston) | ||
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| + | (S,M) any marked surface. Then there exists a cluster algebra associated to it, | ||
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| + | cluster variables <=> arcs | ||
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| + | clusters <-> ideal triangulations | ||
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| + | exchange relations <-> flips | ||
2011년 8월 10일 (수) 07:50 판
n-gon with punctures
tagged triangulation
- two tagged arcs are compatible if
(i) they do not cross
(ii) they are not isotopic except
tagged arc complex is the clique complex where simplices are collections of compatible tagged arcs
\Theorem (Fomin, Shapiro, Thurston)
(S,M) any marked surface. Then there exists a cluster algebra associated to it,
cluster variables <=> arcs
clusters <-> ideal triangulations
exchange relations <-> flips