Algebraic & Geometric Topology Volume 13, issue 2 (2013)

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

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

On the autonomous metric on the group of area-preserving diffeomorphisms of the $2$–disc

Michael Brandenbursky and Jarek Kędra

Algebraic & Geometric Topology 13 (2013) 795–816

DOI: 10.2140/agt.2013.13.795

Bibliography

1	V I Arnold, B A Khesin, Topological methods in hydrodynamics, Applied Mathematical Sciences 125, Springer (1998) MR1612569
2	A Banyaga, Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique, Comment. Math. Helv. 53 (1978) 174 MR490874
3	M Benaim, J M Gambaudo, Metric properties of the group of area preserving diffeomorphisms, Trans. Amer. Math. Soc. 353 (2001) 4661 MR1851187
4	M Bestvina, K Fujiwara, Bounded cohomology of subgroups of mapping class groups, Geom. Topol. 6 (2002) 69 MR1914565
5	P Biran, M Entov, L Polterovich, Calabi quasimorphisms for the symplectic ball, Commun. Contemp. Math. 6 (2004) 793 MR2100764
6	M Brandenbursky, On quasi-morphisms from knot and braid invariants, J. Knot Theory Ramifications 20 (2011) 1397 MR2851716
7	M Brandenbursky, Quasi-morphisms and $L^p$–metrics on groups of volume-preserving diffeomorphisms, J. Topol. Anal. 4 (2012) 255 MR2949242
8	R Brooks, Some remarks on bounded cohomology, from: "Riemann surfaces and related topics" (editors I Kra, B Maskit), Ann. of Math. Stud. 97, Princeton Univ. Press (1981) 53 MR624804
9	D Burago, S Ivanov, L Polterovich, Conjugation-invariant norms on groups of geometric origin, from: "Groups of diffeomorphisms" (editors R Penner, D Kotschick, T Tsuboi, N Kawazumi, T Kitano, Y Mitsumatsu), Adv. Stud. Pure Math. 52, Math. Soc. Japan (2008) 221 MR2509711
10	E Calabi, On the group of automorphisms of a symplectic manifold, from: "Problems in analysis" (editor R C Gunning), Princeton Univ. Press (1970) 1 MR0350776
11	D Calegari, scl, MSJ Memoirs 20, Mathematical Society of Japan (2009) MR2527432
12	J M Gambaudo, É Ghys, Enlacements asymptotiques, Topology 36 (1997) 1355 MR1452855
13	J M Gambaudo, É Ghys, Commutators and diffeomorphisms of surfaces, Ergodic Theory Dynam. Systems 24 (2004) 1591 MR2104597
14	J M Gambaudo, M Lagrange, Topological lower bounds on the distance between area preserving diffeomorphisms, Bol. Soc. Brasil. Mat. 31 (2000) 9 MR1754952
15	H Hofer, On the topological properties of symplectic maps, Proc. Roy. Soc. Edinburgh Sect. A 115 (1990) 25 MR1059642
16	T Ishida, Quasi-morphisms on the group of area-preserving diffeomorphisms of the $2$–disk via braid groups, to appear in Proc. Amer. Math. Soc. arXiv:1204.4056
17	F Lalonde, D McDuff, The geometry of symplectic energy, Ann. of Math. 141 (1995) 349 MR1324138
18	A V Malyutin, Operators in the spaces of pseudocharacters of braid groups, Algebra i Analiz 21 (2009) 136 MR2553045
19	D McDuff, D Salamon, Introduction to symplectic topology, Oxford University Press (1998) MR1698616
20	J Milnor, Lectures on the $h$–cobordism theorem, Princeton Univ. Press (1965) MR0190942
21	L Polterovich, The geometry of the group of symplectic diffeomorphisms, Lectures in Mathematics ETH Zürich 12, Birkhäuser (2001) MR1826128
22	T Tsuboi, The Calabi invariant and the Euler class, Trans. Amer. Math. Soc. 352 (2000) 515 MR1487633