Homeomorphic subsurfaces and the omnipresent arcs
[Sous-surfaces homéomorphes et arcs omniprésents]
Fanoni, Federica1 ; Ghaswala, Tyrone2 ; McLeay, Alan3
1 CNRS, Univ Paris Est Creteil, Univ Gustave Eiffel, LAMA, F-94010 Creteil, (France)
2 Départment de mathématiques, Université du Québec à Montréal, Montréal, (Canada)
3 Mathematics Research Unit, Université du Luxembourg, 4365 Esch-sur-Alzette, (Luxembourg)
Annales Henri Lebesgue, Tome 4 (2021), pp. 1565-1593.

Cet article s’intéresse à plusieurs aspects des arcs sur les surfaces. La première partie s’occupe des aspects topologiques des arcs et de leurs compléments. Nous utilisons les résultats de la première partie pour définir ensuite une action du groupe modulaire sur un sous-graphe du graphe des arcs. Ce sous-graphe ressort naturellement d’une nouvelle caractérisation des surfaces de type infini en termes de sous-surfaces homéomorphes.

In this article, we are concerned with various aspects of arcs on surfaces. In the first part, we deal with topological aspects of arcs and their complements. We use this understanding, in the second part, to construct an interesting action of the mapping class group on a subgraph of the arc graph. This subgraph naturally emerges from a new characterisation of infinite-type surfaces in terms of homeomorphic subsurfaces.

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DOI : 10.5802/ahl.110
Classification : 57K20, 20F65
Mots clés : Infinite-type surfaces, subsurfaces, arcs, arc graphs, mapping class groups.
Fanoni, Federica 1 ; Ghaswala, Tyrone 2 ; McLeay, Alan 3

1 CNRS, Univ Paris Est Creteil, Univ Gustave Eiffel, LAMA, F-94010 Creteil, (France)
2 Départment de mathématiques, Université du Québec à Montréal, Montréal, (Canada)
3 Mathematics Research Unit, Université du Luxembourg, 4365 Esch-sur-Alzette, (Luxembourg) 
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     title = {Homeomorphic subsurfaces and the omnipresent arcs},
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Fanoni, Federica; Ghaswala, Tyrone; McLeay, Alan. Homeomorphic subsurfaces and the omnipresent arcs. Annales Henri Lebesgue, Tome 4 (2021), pp. 1565-1593. doi : 10.5802/ahl.110. http://www.numdam.org/articles/10.5802/ahl.110/

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