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 The Farrell–Jones conjecture for fundamental groups of graphs of abelian groups

2015 ◽  
Vol 9 (3) ◽  
pp. 783-792 ◽  
Author(s):  
Giovanni Gandini ◽  
Sebastian Meinert ◽  
Henrik Rüping
Keyword(s):  
Abelian Groups ◽  
Fundamental Groups

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 Which Abelian Groups Can be Fundamental Groups of Regions in Euclidean Spaces?

1974 ◽  
Vol 26 (1) ◽  
pp. 7-18
Author(s):  
Bai Ching Chang
Keyword(s):  
Finite Number ◽  
Abelian Groups ◽  
Special Consideration ◽  
Fundamental Groups ◽  
Euclidean Spaces ◽  
Dimension 2

It is known that there are a lot of properties of the group of a knot in S3 which fail to generalize to the group of a knotted sphere in S4; among them are included Dehn's lemma, Hopf's conjecture, and the aspherity of knots. In this paper, we shall investigate the properties of the fundamental groups of regions in S3 and in S4, with examples to show that they are not quite the same. Some special consideration will be given to regions that are the complements in S3 or in S4 of a finite number of tamely imbedded manifolds of co-dimension 2, and, more generally, to regions that are the complements of subcomplexes in S3 or in S4.

scholarly journals The geometry and fundamental groups of solenoid complements

2015 ◽  
Vol 24 (14) ◽  
pp. 1550069 ◽  
Author(s):  
Gregory R. Conner ◽  
Mark Meilstrup ◽  
Dušan Repovš
Keyword(s):  
Fundamental Group ◽  
Inverse Limit ◽  
Abelian Groups ◽  
Inverse Limits ◽  
Fundamental Groups ◽  
Three Space

A solenoid is an inverse limit of circles. When a solenoid is embedded in three space, its complement is an open three manifold. We discuss the geometry and fundamental groups of such manifolds, and show that the complements of different solenoids (arising from different inverse limits) have different fundamental groups. Embeddings of the same solenoid can give different groups; in particular, the nicest embeddings are unknotted at each level, and give an Abelian fundamental group, while other embeddings have non-Abelian groups. We show using geometry that every solenoid has uncountably many embeddings with nonhomeomorphic complements.

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
Sign in / Sign up

Export Citation Format

Share Document