Asymptotic dimensions of the arc graphs and disk graphs

HIGHLIGHTS

  • Who: Koji Fujiwara and Saul Schleimer from the (UNIVERSITY) have published the Article: Asymptotic dimensions of the arc graphs and disk graphs, in the Journal: (JOURNAL)

SUMMARY

    The authors define the arc graph A.S/ similarly: A.0/.S/ is the set of proper isotopy classes of essential arcs in S. Again the authors have an edge.˛; ˇ/ 2 A.1/ exactly when ˛ and ˇ are distinct and i.˛; ˇ/ D 0. JdX.˛; / dX. c.˛/; c. //j Proof Suppose that ˇ 2 A.S; / has dA.˛; ˇ/ 2 and ˇ is carried by some witness Y with 0.Y . . .

     

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