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Glasnik matematički, Vol. 58 No. 1, 2023.

Original scientific paper

https://doi.org/10.3336/gm.58.1.09

Big flip graphs and their automorphism groups

Assaf Bar-Natan orcid id orcid.org/0000-0002-2715-788X ; Department of Mathematics, Brandeis University, 415 South Street, Waltham, MA 02453, USA
Advay Goel ; Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
Brendan Halstead ; nbsp
Paul Hamrick ; UNC Chapel Hill
Sumedh Shenoy ; Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA
Rishi Verma ; Stanford University

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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.

Keywords

Flip graphs, infinite-type surfaces, mapping class groups, Ivanov

Hrčak ID:

304396

URI

https://hrcak.srce.hr/304396

Publication date:

20.6.2023.

Visits: 499 *

Publication date: 30 June 2023

Volume: Vol 58

Issue: Svezak 1

Pages: 125-134

DOI: 10.3336/gm.58.1.09

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Flip graphs, infinite-type surfaces, mapping class groups, Ivanov

Big flip graphs and their automorphism groups

Assaf Bar-Natan[1]

Email: assafbarnatan@gmail.com

Advay Goel[2]

Email: advayg@mit.edu

Brendan Halstead[3]

Email: brendanhalstead23@gmail.com

Paul Hamrick[4]

Email: hamri@unc.ed

Sumedh Shenoy[5]

Email: sshenoy@mit.edu

Rishi Verma[6]

Email: verma.rishiraj@gmail.com

 

[1] Department of Mathematics, Brandeis University, 415 South Street, Waltham, MA 02453, USA

[2] Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA

[3] nbsp;

[4] UNC Chapel Hill

[5] Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, USA

[6] Stanford University

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.

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