"Surfaces with punctures"의 두 판 사이의 차이
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imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
imported>Pythagoras0 잔글 (찾아 바꾸기 – “</h5>” 문자열을 “==” 문자열로) |
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| 7번째 줄: | 7번째 줄: | ||
| − | ==notions | + | ==notions== |
* once-punctured monogon | * once-punctured monogon | ||
| 19번째 줄: | 19번째 줄: | ||
| − | ==tagged triangulation | + | ==tagged triangulation== |
* 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 | + | ==tagged arc complex== |
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: | ||
| − | == | + | == == |
2012년 10월 28일 (일) 14:48 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