Author:
Bar-Natan Assaf, ,Goel Advay,Halstead Brendan,Hamrick Paul,Shenoy Sumedh,Verma Rishi, , , , ,
Abstract
In this paper, we study the relationship between the mapping class
group of an infinite-type surface and the simultaneous flip graph,
a variant of the flip graph for infinite-type surfaces defined by
Fossas and Parlier [6]. We show that the extended
mapping class group is isomorphic to a proper subgroup of the
automorphism group of the flip graph, unlike in the finite-type
case. This shows that Ivanov's metaconjecture, which states that
any “sufficiently rich" object associated to a finite-type surface
has the extended mapping class group as its automorphism group, does
not extend to simultaneous flip graphs of infinite-type surfaces.
Publisher
University of Zagreb, Faculty of Science, Department of Mathematics
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