Algebraic & Geometric Topology Volume 23, issue 2 (2023)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Other MSP journals

A short proof that the $L^p$–diameter of $\operatorname{Diff}_0(S,\mathrm{area})$ is infinite

Michał Marcinkowski

Algebraic & Geometric Topology 23 (2023) 883–893

DOI: 10.2140/agt.2023.23.883

Bibliography

1	V I Arnold, B A Khesin, Topological methods in hydrodynamics, 125, Springer (1998) MR1612569
2	P Bellingeri, On presentations of surface braid groups, J. Algebra 274 (2004) 543 MR2043362
3	M Brandenbursky, Quasi-morphisms and L^p–metrics on groups of volume-preserving diffeomorphisms, J. Topol. Anal. 4 (2012) 255 MR2949242
4	M Brandenbursky, J Kędra, Quasi-isometric embeddings into diffeomorphism groups, Groups Geom. Dyn. 7 (2013) 523 MR3095706
5	M Brandenbursky, M Marcinkowski, Bounded cohomology of transformation groups, Math. Ann. 382 (2022) 1181 MR4403221
6	M Brandenbursky, E Shelukhin, On the L^p–geometry of autonomous Hamiltonian diffeomorphisms of surfaces, Math. Res. Lett. 22 (2015) 1275 MR3488375
7	M Brandenbursky, E Shelukhin, The L^p–diameter of the group of area-preserving diffeomorphisms of S², Geom. Topol. 21 (2017) 3785 MR3693576
8	Y Eliashberg, T Ratiu, The diameter of the symplectomorphism group is infinite, Invent. Math. 103 (1991) 327 MR1085110
9	J M Gambaudo, M Lagrange, Topological lower bounds on the distance between area preserving diffeomorphisms, Bol. Soc. Brasil. Mat. 31 (2000) 9 MR1754952
10	S h Kim, T Koberda, Anti-trees and right-angled Artin subgroups of braid groups, Geom. Topol. 19 (2015) 3289 MR3447104
11	E Shelukhin, The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures, Comment. Math. Helv. 89 (2014) 69 MR3177909
12	A I Shnirelman, The geometry of the group of diffeomorphisms and the dynamics of an ideal incompressible fluid, Mat. Sb. 128(170) (1985) 82 MR805697
13	A I Shnirelman, Generalized fluid flows, their approximation and applications, Geom. Funct. Anal. 4 (1994) 586 MR1296569