Volume 20, issue 6 (2020)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Finite rigid sets in arc complexes

Emily Shinkle

Algebraic & Geometric Topology 20 (2020) 3127–3145
DOI: 10.2140/agt.2020.20.3127
Bibliography
1 J Aramayona, Simplicial embeddings between pants graphs, Geom. Dedicata 144 (2010) 115 MR2580421
2 J Aramayona, T Koberda, H Parlier, Injective maps between flip graphs, Ann. Inst. Fourier (Grenoble) 65 (2015) 2037 MR3449205
3 J Aramayona, C J Leininger, Finite rigid sets in curve complexes, J. Topol. Anal. 5 (2013) 183 MR3062946
4 J Aramayona, C J Leininger, Exhausting curve complexes by finite rigid sets, Pacific J. Math. 282 (2016) 257 MR3478935
5 F Atalan, M Korkmaz, Automorphisms of curve complexes on nonorientable surfaces, Groups Geom. Dyn. 8 (2014) 39 MR3209702
6 M C Bell, V Disarlo, R Tang, Cubical geometry in the polygonalisation complex, Math. Proc. Cambridge Philos. Soc. 167 (2019) 1 MR3968817
7 T E Brendle, D Margalit, Normal subgroups of mapping class groups and the metaconjecture of Ivanov, J. Amer. Math. Soc. 32 (2019) 1009 MR4013739
8 V Disarlo, Combinatorial rigidity of arc complexes, preprint (2015) arXiv:1505.08080
9 J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157 MR830043
10 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
11 J Hernández Hernández, Edge-preserving maps of curve graphs, Topology Appl. 246 (2018) 83 MR3834842
12 J Hernández Hernández, C J Leininger, R Maungchang, Finite rigid subgraphs of pants graphs, preprint (2019) arXiv:1907.12734
13 S Ilbira, M Korkmaz, Finite rigid sets in curve complexes of nonorientable surfaces, Geom. Dedicata 206 (2020) 83 MR4091539
14 E Irmak, Complexes of nonseparating curves and mapping class groups, Michigan Math. J. 54 (2006) 81 MR2214789
15 E Irmak, Injective simplicial maps of the complex of arcs on nonorientable surfaces, Algebr. Geom. Topol. 9 (2009) 2055 MR2551662
16 E Irmak, Superinjective simplicial maps of the complexes of curves on nonorientable surfaces, Turkish J. Math. 36 (2012) 407 MR2993573
17 E Irmak, On simplicial maps of the complexes of curves of nonorientable surfaces, Algebr. Geom. Topol. 14 (2014) 1153 MR3180830
18 E Irmak, Exhausting curve complexes by finite rigid sets on nonorientable surfaces, preprint (2019) arXiv:1906.09913
19 E Irmak, Exhausting curve complexes by finite superrigid sets on nonorientable surfaces, preprint (2019) arXiv:1903.04926
20 E Irmak, M Korkmaz, Automorphisms of the Hatcher–Thurston complex, Israel J. Math. 162 (2007) 183 MR2365859
21 E Irmak, J D McCarthy, Injective simplicial maps of the arc complex, Turkish J. Math. 34 (2010) 339 MR2681579
22 E Irmak, L Paris, Superinjective simplicial maps of the two-sided curve complexes on nonorientable surfaces, Fund. Math. 249 (2020) 211 MR4078215
23 N V Ivanov, Automorphisms of complexes of curves and of Teichmüller spaces, Int. Math. Res. Not. 1997 (1997) 651 MR1460387
24 N V Ivanov, Fifteen problems about the mapping class groups, from: "Problems on mapping class groups and related topics" (editor B Farb), Proc. Sympos. Pure Math. 74, Amer. Math. Soc. (2006) 71 MR2264532
25 M Korkmaz, Automorphisms of complexes of curves on punctured spheres and on punctured tori, Topology Appl. 95 (1999) 85 MR1696431
26 M Korkmaz, A Papadopoulos, On the arc and curve complex of a surface, Math. Proc. Cambridge Philos. Soc. 148 (2010) 473 MR2609303
27 M Korkmaz, A Papadopoulos, On the ideal triangulation graph of a punctured surface, Ann. Inst. Fourier (Grenoble) 62 (2012) 1367 MR3025746
28 F Luo, Automorphisms of the complex of curves, Topology 39 (2000) 283 MR1722024
29 D Margalit, Automorphisms of the pants complex, Duke Math. J. 121 (2004) 457 MR2040283
30 R Maungchang, Exhausting pants graphs of punctured spheres by finite rigid sets, J. Knot Theory Ramifications 26 (2017) MR3735406
31 R Maungchang, Finite rigid subgraphs of the pants graphs of punctured spheres, Topology Appl. 237 (2018) 37 MR3760775
32 J D McCarthy, A Papadopoulos, Simplicial actions of mapping class groups, from: "Handbook of Teichmüller theory, III" (editor A Papadopoulos), IRMA Lect. Math. Theor. Phys. 17, Eur. Math. Soc. (2012) 297 MR2952767
33 A McLeay, Geometric normal subgroups in mapping class groups of punctured surfaces, New York J. Math. 25 (2019) 839 MR4012570
34 L Mosher, Tiling the projective foliation space of a punctured surface, Trans. Amer. Math. Soc. 306 (1988) 1 MR927683
35 P Schmutz Schaller, Mapping class groups of hyperbolic surfaces and automorphism groups of graphs, Compos. Math. 122 (2000) 243 MR1781329
36 K J Shackleton, Combinatorial rigidity in curve complexes and mapping class groups, Pacific J. Math. 230 (2007) 217 MR2318453