Algebraic & Geometric Topology Volume 17, issue 2 (2017)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs

Daniel Cristofaro-Gardiner, David Frenkel and Felix Schlenk

Algebraic & Geometric Topology 17 (2017) 1189–1260

DOI: 10.2140/agt.2017.17.1189

Bibliography

1	V I Arnol’d, S M Guseĭn-Zade, A N Varchenko, Singularities of differentiable maps, II, 83, Birkhäuser (1988) MR966191
2	P Biran, Symplectic packing in dimension 4, Geom. Funct. Anal. 7 (1997) 420 MR1466333
3	P Biran, A stability property of symplectic packing, Invent. Math. 136 (1999) 123 MR1681101
4	M Burkhart, P Panescu, M Timmons, Symplectic embeddings of 4–dimensional ellipsoids into polydiscs, Involve 10 (2017) 219
5	O Buse, R Hind, Symplectic embeddings of ellipsoids in dimension greater than four, Geom. Topol. 15 (2011) 2091 MR2860988
6	O Buse, R Hind, Ellipsoid embeddings and symplectic packing stability, Compos. Math. 149 (2013) 889 MR3069365
7	O Buse, R Hind, E Opshtein, Packing stability for symplectic 4–manifolds, Trans. Amer. Math. Soc. 368 (2016) 8209 MR3546797
8	O Buse, M Pinsonnault, Packing numbers of rational ruled four-manifolds, J. Symplectic Geom. 11 (2013) 269 MR3046492
9	K Choi, D Cristofaro-Gardiner, D Frenkel, M Hutchings, V G B Ramos, Symplectic embeddings into four-dimensional concave toric domains, J. Topol. 7 (2014) 1054 MR3286897
10	D Cristofaro-Gardiner, ECH capacities and dynamics, in preparation
11	D Cristofaro-Gardiner, Symplectic embeddings from concave toric domains into convex ones, preprint (2014) arXiv:1409.4378
12	D Cristofaro-Gardiner, R Hind, Symplectic embeddings of products, preprint (2015) arXiv:1508.02659
13	D Cristofaro-Gardiner, A Kleinman, Ehrhart polynomials and symplectic embeddings of ellipsoids, preprint (2013) arXiv:1307.5493
14	D Frenkel, D Müller, Symplectic embeddings of 4–dim ellipsoids into cubes, J. Symplectic Geom. 13 (2015) 765 MR3480057
15	M Gromov, Pseudo holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307 MR809718
16	R Hind, Some optimal embeddings of symplectic ellipsoids, J. Topol. 8 (2015) 871 MR3394319
17	R Hind, E Kerman, New obstructions to symplectic embeddings, Invent. Math. 196 (2014) 383 MR3193752
18	M Hutchings, Quantitative embedded contact homology, J. Differential Geom. 88 (2011) 231 MR2838266
19	M Hutchings, Recent progress on symplectic embedding problems in four dimensions, Proc. Natl. Acad. Sci. USA 108 (2011) 8093 MR2806644
20	Y Karshon, L Kessler, Distinguishing symplectic blowups of the complex projective plane, preprint (2014) arXiv:1407.5312
21	B H Li, T J Li, Symplectic genus, minimal genus and diffeomorphisms, Asian J. Math. 6 (2002) 123 MR1902650
22	T J Li, A K Liu, Uniqueness of symplectic canonical class, surface cone and symplectic cone of 4–manifolds with B⁺ = 1, J. Differential Geom. 58 (2001) 331 MR1913946
23	D McDuff, Symplectic embeddings of 4–dimensional ellipsoids, J. Topol. 2 (2009) 1 MR2499436
24	D McDuff, The Hofer conjecture on embedding symplectic ellipsoids, J. Differential Geom. 88 (2011) 519 MR2844441
25	D McDuff, L Polterovich, Symplectic packings and algebraic geometry, Invent. Math. 115 (1994) 405 MR1262938
26	D McDuff, F Schlenk, The embedding capacity of 4–dimensional symplectic ellipsoids, Ann. of Math. 175 (2012) 1191 MR2912705
27	F Schlenk, Symplectic embeddings of ellipsoids, Israel J. Math. 138 (2003) 215 MR2031958
28	F Schlenk, Embedding problems in symplectic geometry, 40, de Gruyter (2005) MR2147307
29	F Schlenk, Symplectic embedding problem, old and new, book in preparation
30	P Seidel, Lagrangian two-spheres can be symplectically knotted, J. Differential Geom. 52 (1999) 145 MR1743463