scholarly journals symplectically aspherical manifolds with nontrivial $\pi_2$

1998 ◽  
Vol 5 (5) ◽  
pp. 599-603 ◽  
Author(s):  
Robert E. Gompf
Keyword(s):  
Aspherical Manifolds ◽  
Symplectically Aspherical

scholarly journals Length minimizing Hamiltonian paths for symplectically aspherical manifolds

2003 ◽  
Vol 53 (5) ◽  
pp. 1503-1526 ◽  
Author(s):  
Ely Kerman ◽  
François Lalonde
Keyword(s):  
Hamiltonian Paths ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

scholarly journals Symplectically aspherical manifolds

2008 ◽  
Vol 3 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Jarek Kędra ◽  
Yuli Rudyak ◽  
Aleksy Tralle
Keyword(s):  
Aspherical Manifolds ◽  
Symplectically Aspherical

scholarly journals On fundamental groups of symplectically aspherical manifolds II: Abelian groups

2007 ◽  
Vol 256 (4) ◽  
pp. 825-835 ◽  
Author(s):  
J. Kȩdra ◽  
Yu. Rudyak ◽  
A. Tralle
Keyword(s):  
Abelian Groups ◽  
Fundamental Groups ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

scholarly journals On fundamental groups of symplectically aspherical manifolds

2004 ◽  
Vol 248 (4) ◽  
pp. 805-826 ◽  
Author(s):  
R. Ib��ez ◽  
J. Kedra ◽  
Yu. Rudyak ◽  
A. Tralle
Keyword(s):  
Fundamental Groups ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

scholarly journals Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms

2019 ◽  
Vol 11 (02) ◽  
pp. 467-498
Author(s):  
D. Alvarez-Gavela ◽  
V. Kaminker ◽  
A. Kislev ◽  
K. Kliakhandler ◽  
A. Pavlichenko ◽  
...  
Keyword(s):  
Free Group ◽  
Free Groups ◽  
Asymptotic Cone ◽  
Asymptotic Cones ◽  
Hamiltonian Diffeomorphisms ◽  
Symplectic Surface ◽  
Genus Formula ◽  
Hofer Metric ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

Given a symplectic surface [Formula: see text] of genus [Formula: see text], we show that the free group with two generators embeds into every asymptotic cone of [Formula: see text], where [Formula: see text] is the Hofer metric. The result stabilizes to products with symplectically aspherical manifolds.

scholarly journals THE GYSIN EXACT SEQUENCE FOR S1-EQUIVARIANT SYMPLECTIC HOMOLOGY

2013 ◽  
Vol 05 (04) ◽  
pp. 361-407 ◽  
Author(s):  
FRÉDÉRIC BOURGEOIS ◽  
ALEXANDRU OANCEA
Keyword(s):  
Exact Sequence ◽  
Parameter Space ◽  
Contact Boundary ◽  
Important Ingredient ◽  
Symplectic Homology ◽  
Finite Dimensional ◽  
Type Construction ◽  
Hamiltonian Functions ◽  
Aspherical Manifolds ◽  
Symplectically Aspherical

We define S1-equivariant symplectic homology for symplectically aspherical manifolds with contact boundary, using a Floer-type construction first proposed by Viterbo. We show that it is related to the usual symplectic homology by a Gysin exact sequence. As an important ingredient of the proof, we define a parametrized version of symplectic homology, corresponding to families of Hamiltonian functions indexed by a finite dimensional smooth parameter space.

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