Surfaces with punctures
Pythagoras0 (토론 | 기여)님의 2020년 12월 28일 (월) 04:15 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