scholarly journals Aspherical manifolds with relatively hyperbolic fundamental groups

2007 ◽  
Vol 129 (1) ◽  
pp. 119-144 ◽  
Author(s):  
Igor Belegradek
Keyword(s):  
Fundamental Groups ◽  
Aspherical Manifolds ◽  
Relatively Hyperbolic

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 Novikov Conjectures and Relative Hyperbolicity

1999 ◽  
Vol 85 (2) ◽  
pp. 169 ◽  
Author(s):  
Boris Goldfarb
Keyword(s):  
Symmetric Spaces ◽  
Large Family ◽  
Hyperbolic Groups ◽  
Fundamental Groups ◽  
Arithmetic Groups ◽  
Relatively Hyperbolic Groups ◽  
Rank One ◽  
Higher Rank ◽  
Relatively Hyperbolic ◽  
Relative Hyperbolicity

We consider a class of relatively hyperbolic groups in the sense of Gromov and use an argument modeled after Carlsson-Pedersen to prove Novikov conjectures for these groups. This proof is related to [16,17] which dealt with arithmetic lattices in rank one symmetric spaces and some other arithmetic groups of higher rank. Here whe view the rank one lattices in this different larger context of relativve hyperbolicity which also inclues fundamental groups of pinched hyperbolic manifolds. Another large family of groups from this class is produced using combinatorial hyperbolization techniques.

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 ON A GENERALIZATION OF DEHN'S ALGORITHM

2008 ◽  
Vol 18 (07) ◽  
pp. 1137-1177 ◽  
Author(s):  
OLIVER GOODMAN ◽  
MICHAEL SHAPIRO
Keyword(s):  
Finite Groups ◽  
Nilpotent Groups ◽  
Hyperbolic Groups ◽  
Fundamental Groups ◽  
Closure Properties ◽  
Relatively Hyperbolic Groups ◽  
Geometrically Finite ◽  
Geometrically Finite Groups ◽  
Relatively Hyperbolic ◽  
Infinite Subgroup

Viewing Dehn's algorithm as a rewriting system, we generalize to allow an alphabet containing letters which do not necessarily represent group elements. This extends the class of groups for which the algorithm solves the word problem to include finitely generated nilpotent groups, many relatively hyperbolic groups including geometrically finite groups and fundamental groups of certain geometrically decomposable 3-manifolds. The class has several nice closure properties. We also show that if a group has an infinite subgroup and one of exponential growth, and they commute, then it does not admit such an algorithm. We dub these Cannon's algorithms.

scholarly journals Asymptotically isometric metrics on relatively hyperbolic groups and marked length spectrum

2015 ◽  
Vol 07 (02) ◽  
pp. 345-359 ◽  
Author(s):  
Koji Fujiwara
Keyword(s):  
Hyperbolic Group ◽  
Length Spectrum ◽  
Hyperbolic Groups ◽  
Fundamental Groups ◽  
Relatively Hyperbolic Groups ◽  
Universal Covers ◽  
Relatively Hyperbolic Group ◽  
Marked Length Spectrum ◽  
Isospectral Problem ◽  
Relatively Hyperbolic

We prove asymptotically isometric, coarsely geodesic metrics on a toral relatively hyperbolic group are coarsely equal. The theorem applies to all lattices in SO (n, 1). This partly verifies a conjecture by Margulis. In the case of hyperbolic groups/spaces, our result generalizes a theorem by Furman and a theorem by Krat. We discuss an application to the isospectral problem for the length spectrum of Riemannian manifolds. The positive answer to this problem has been known for several cases. Most of them have hyperbolic fundamental groups. We do not solve the isospectral problem in the original sense, but prove the universal covers are (1, C)-quasi-isometric if the fundamental group is a toral relatively hyperbolic group.

Equations in Algebras

2018 ◽  
Vol 28 (08) ◽  
pp. 1517-1533 ◽  
Author(s):  
Olga Kharlampovich ◽  
Alexei Myasnikov
Keyword(s):  
Hyperbolic Groups ◽  
Fundamental Groups ◽  
Associative Algebras ◽  
Relatively Hyperbolic Groups ◽  
Transitive Groups ◽  
Right Angled Artin Groups ◽  
Graph Groups ◽  
Commutative Transitive ◽  
Relatively Hyperbolic ◽  
Torsion Free

We show that the Diophantine problem (decidability of equations) is undecidable in free associative algebras over any field and in the group algebras over any field of a wide variety of torsion free groups, including toral relatively hyperbolic groups, right-angled Artin groups, commutative transitive groups, the fundamental groups of various graph groups, etc.

scholarly journals Fundamental groups of aspherical manifolds and maps of non-zero degree

2018 ◽  
Vol 12 (2) ◽  
pp. 637-677 ◽  
Author(s):  
Christoforos Neofytidis
Keyword(s):  
Fundamental Groups ◽  
Zero Degree ◽  
Aspherical Manifolds

Filling words in fundamental groups of Riemann surfaces

2013 ◽  
Vol 50 (1) ◽  
pp. 31-50
Author(s):  
C. Zhang
Keyword(s):  
Riemann Surface ◽  
Fundamental Group ◽  
Riemann Surfaces ◽  
Fundamental Groups ◽  
Closed Geodesics ◽  
New Words

The purpose of this article is to utilize some exiting words in the fundamental group of a Riemann surface to acquire new words that are represented by filling closed geodesics.

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