"Surfaces with punctures"의 두 판 사이의 차이

2011년 8월 10일 (수) 08:08 판

surface with punctures

replace ideal triangulation by 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 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

@@ 1번째 줄: / 1번째 줄: @@
-n-gon with punctures
+surface with punctures
+replace ideal triangulation by tagged triangulation
+<h5>notions</h5>
+* once-punctured monogon
+* once-punctured n-gon
+* self-folded
+* tagged arc
@@ 8번째 줄: / 21번째 줄: @@
 *  two tagged arcs are compatible if<br> (i) they do not cross<br> (ii) they are not isotopic except<br>
+*  tagged triangulation<br>
+** maximal collection of compatible tagged arcs
+<h5>tagged arc complex</h5>
 tagged arc complex is the clique complex where simplices are collections of compatible tagged arcs
@@ 23번째 줄: / 40번째 줄: @@
 (S,M) any marked surface.  Then there exists a cluster algebra associated to it,
-cluster variables <=> arcs
+tagged arc complex = cluster complex
-clusters <-> ideal triangulations
+tagged arcs,- <=> cluster variables
-exchange relations <-> flips
+tagged flips <-> mutations