"Surfaces with punctures"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| 7번째 줄: | 7번째 줄: | ||
| − | + | ==notions</h5> | |
* once-punctured monogon | * once-punctured monogon | ||
| 19번째 줄: | 19번째 줄: | ||
| − | + | ==tagged triangulation</h5> | |
* two tagged arcs are compatible if<br> (i) they do not cross<br> (ii) they are not isotopic except<br> | * two tagged arcs are compatible if<br> (i) they do not cross<br> (ii) they are not isotopic except<br> | ||
| 29번째 줄: | 29번째 줄: | ||
| − | + | ==tagged arc complex</h5> | |
tagged arc complex is the clique complex where simplices are collections of compatible tagged arcs | tagged arc complex is the clique complex where simplices are collections of compatible tagged arcs | ||
| 53번째 줄: | 53번째 줄: | ||
| − | + | == </h5> | |
2012년 10월 28일 (일) 14:02 판
surface with punctures
replace ideal triangulation by tagged triangulation
==notions
- once-punctured monogon
- once-punctured n-gon
- self-folded
- tagged arc
- radius
==tagged triangulation
- two tagged arcs are compatible if
(i) they do not cross
(ii) they are not isotopic except - tagged triangulation
- maximal collection of compatible tagged arcs
==tagged arc complex
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,
tagged arc complex = cluster complex
tagged arcs,- <=> cluster variables
tagged flips <-> mutations
==