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

A rational invariant for certain infinite discrete groups

1993 ◽  
Vol 113 (3) ◽  
pp. 473-478
Author(s):  
F. E. A. Johnson
Keyword(s):  
Euler Characteristic ◽  
Discrete Groups ◽  
Fundamental Groups ◽  
Intersection Form ◽  
Absolute Value ◽  
Rational Invariant ◽  
The Absolute ◽  
Image Position ◽  
Aspherical Manifolds

We introduce a rational-valued invariant which is capable of distinguishing between the commensurability classes of certain discrete groups, namely, the fundamental groups of smooth closed orientable aspherical manifolds of dimensional 4k(k ≥ 1) whose Euler characteristic χ(Λ) is non-zero. The invariant in question is the quotientwhere Sign (Λ) is the absolute value of the signature of the intersection formand [Λ] is a generator of H4k(Λ; ℝ).

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 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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