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We obtain new obstructions to symplectic embeddings of the four-dimensional polydisk P(a,1) into the ball B(c) for 2 ≤ a ≤ (7 − 1)∕(7 − 2) ≈ 2.549, extending work done by Hind and Lisi and by Hutchings. Schlenk’s folding construction permits us to conclude our bound on c is optimal. Our proof makes use of the combinatorial criterion necessary for one “convex toric domain” to symplectically embed into another introduced by Hutchings (2016). We also observe that the computational complexity of this criterion can be reduced from O(2n) to O(n2).
Keywords: symplectic embeddings, embedded contact homology
Christianson, Katherine 1 ; Nelson, Jo 2
@article{10_2140_agt_2018_18_2151,
author = {Christianson, Katherine and Nelson, Jo},
title = {Symplectic embeddings of four-dimensional polydisks into balls},
journal = {Algebraic and Geometric Topology},
pages = {2151--2178},
publisher = {mathdoc},
volume = {18},
number = {4},
year = {2018},
doi = {10.2140/agt.2018.18.2151},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2151/}
}
TY - JOUR AU - Christianson, Katherine AU - Nelson, Jo TI - Symplectic embeddings of four-dimensional polydisks into balls JO - Algebraic and Geometric Topology PY - 2018 SP - 2151 EP - 2178 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2151/ DO - 10.2140/agt.2018.18.2151 ID - 10_2140_agt_2018_18_2151 ER -
%0 Journal Article %A Christianson, Katherine %A Nelson, Jo %T Symplectic embeddings of four-dimensional polydisks into balls %J Algebraic and Geometric Topology %D 2018 %P 2151-2178 %V 18 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.2151/ %R 10.2140/agt.2018.18.2151 %F 10_2140_agt_2018_18_2151
Christianson, Katherine; Nelson, Jo. Symplectic embeddings of four-dimensional polydisks into balls. Algebraic and Geometric Topology, Tome 18 (2018) no. 4, pp. 2151-2178. doi: 10.2140/agt.2018.18.2151
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