Automatic continuity for homeomorphism groups and applications

Geometry and Topology

Volumn 20, Issue 5, 2016, Pages 3033-3056

  Mann, Kathryn ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Automatic continuity; Germs of homeomorphisms; Homeomorphism groups

Indexed keywords

EID: 84992125757     PISSN: 14653060     EISSN: 13640380     Source Type: Journal    
DOI: 10.2140/gt.2016.20.3033     Document Type: Article

References (22)

1. RD Anderson, The algebraic simplicity of certain groups of homeomorphisms, Amer. J. Math. 80 (1958) 955–963 MR0098145
2. H Becker, AS Kechris, The descriptive set theory of Polish group actions, London Math. Soc. Lect. Note Ser. 232, Cambridge Univ. Press (1996) MR1425877
3. D Burago, S Ivanov, L Polterovich, Conjugation-invariant norms on groups of geometric origin, from: “Groups of diffeomorphisms”, (R Penner, D Kotschick, T Tsuboi, N Kawazumi, T Kitano, Y Mitsumatsu, editors), Adv. Stud. Pure Math. 52, Math. Soc. Japan, Tokyo (2008) 221–250 MR2509711 arXiv:0710.1412
4. B Deroin, A Navas, A Rivas, Groups, orders, and dynamics, preprint (2014) arXiv: 1408.5805
5. R.D Edwards, R.C Kirby, Deformations of spaces of imbeddings, Ann. Math. 93 (1971) 63–88 MR0283802
6. D Epstein, V Markovic, Extending homeomorphisms of the circle to quasiconformal homeomorphisms of the disk, Geom. Topol. 11 (2007) 517–595 MR2302497
7. MW Hirsch, Differential topology, Graduate Texts in Mathematics 33, Springer, New York (1994) MR1336822
8. S Hurtado, Continuity of discrete homomorphisms of diffeomorphism groups, Geom. Topol. 19 (2015) 2117–2154 MR3375524
9. R.R Kallman, Uniqueness results for homeomorphism groups, Trans. Amer. Math. Soc. 295 (1986) 389–396 MR831205
10. R.R Kallman, Every reasonably sized matrix group is a subgroup of S1, Fund. Math. 164 (2000) 35–40 MR1784652
11. A.S Kechris, Classical descriptive set theory, Graduate Texts in Mathematics 156, Springer, New York (1995) MR1321597
12. R.C Kirby, Stable homeomorphisms and the annulus conjecture, Ann. of Math. 89 (1969) 575–582 MR0242165
13. J Kittrell, T Tsankov, Topological properties of full groups, Ergodic Theory Dynam. Systems 30 (2010) 525–545 MR2599891
14. K Mann, Left-orderable groups that don’t act on the line, Math. Z. 280 (2015) 905–918 MR3369358
15. A Navas, A finitely generated, locally indicable group with no faithful action by C1 diffeomorphisms of the interval, Geom. Topol. 14 (2010) 573–584 MR2602845
16. F Quinn, Ends of maps, III: Dimensions 4 and 5, J. Differential Geom. 17 (1982) 503–521 MR679069
17. C Rosendal, Automatic continuity in homeomorphism groups of compact 2–manifolds, Israel J. Math. 166 (2008) 349–367 MR2430439
18. C Rosendal, S Solecki, Automatic continuity of homomorphisms and fixed points on metric compacta, Israel J. Math. 162 (2007) 349–371 MR2365867
19. M Sabok, Automatic continuity for isometry groups, preprint (2013) arXiv: 1312.5141v1
20. T Tsankov, Automatic continuity for the unitary group, Proc. Amer. Math. Soc. 141 (2013) 3673–3680 MR3080189
21. T Tsuboi, Homeomorphism groups of commutator width one, Proc. Amer. Math. Soc. 141 (2013) 1839–1847 MR3020870
22. JV Whittaker, On isomorphic groups and homeomorphic spaces, Ann. of Math. 78 (1963) 74–91 MR0150750