"Surfaces with punctures"의 두 판 사이의 차이

2020년 12월 28일 (월) 04:15 기준 최신판

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>tagged triangulation</h5>
-*  two tagged arcs are compatible if<br> (i) they do not cross<br> (ii) they are not isotopic except<br>
+==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,
+(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
-cluster variables <=> arcs
-clusters <-> ideal triangulations
-exchange relations <-> flips
+== ==
+[[분류:개인노트]]
+[[분류:cluster algebra]]
+[[분류:math and physics]]
+[[분류:math]]
+[[분류:migrate]]