"Surfaces with punctures"의 두 판 사이의 차이
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imported>Pythagoras0 |
Pythagoras0 (토론 | 기여) |
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| (같은 사용자의 중간 판 하나는 보이지 않습니다) | |||
| 3번째 줄: | 3번째 줄: | ||
replace ideal triangulation by tagged triangulation | replace ideal triangulation by tagged triangulation | ||
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==notions== | ==notions== | ||
| 15번째 줄: | 15번째 줄: | ||
* radius | * radius | ||
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==tagged triangulation== | ==tagged triangulation== | ||
| − | * two tagged arcs are compatible if | + | * two tagged arcs are compatible if (i) they do not cross (ii) they are not isotopic except |
| − | * tagged triangulation | + | * tagged triangulation |
** maximal collection of compatible tagged arcs | ** maximal collection of compatible tagged arcs | ||
| − | + | ||
| − | + | ||
==tagged arc complex== | ==tagged arc complex== | ||
| 33번째 줄: | 33번째 줄: | ||
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 | ||
| − | + | ||
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\Theorem (Fomin, Shapiro, Thurston) | \Theorem (Fomin, Shapiro, Thurston) | ||
| − | (S,M) any marked surface. | + | (S,M) any marked surface. Then there exists a cluster algebra associated to it, |
tagged arc complex = cluster complex | tagged arc complex = cluster complex | ||
| − | tagged arcs,- <=> cluster | + | tagged arcs,- <=> cluster variables |
tagged flips <-> mutations | tagged flips <-> mutations | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | == | + | == == |
[[분류:개인노트]] | [[분류:개인노트]] | ||
[[분류:cluster algebra]] | [[분류:cluster algebra]] | ||
2020년 12월 28일 (월) 04:15 기준 최신판
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