scholarly journals Quasiconvex subgroups of negatively curved groups

1994 ◽  
Vol 95 (3) ◽  
pp. 297-301 ◽  
Author(s):  
Michael L. Mihalik ◽  
Williams Towle
Keyword(s):  
Negatively Curved ◽  
Quasiconvex Subgroups

On intersections of conjugate subgroups

2017 ◽  
Vol 27 (04) ◽  
pp. 403-419 ◽  
Author(s):  
Rita Gitik
Keyword(s):  
Conjugacy Class ◽  
Generating Set ◽  
Explicit Algorithm ◽  
Negatively Curved ◽  
Coset Graph ◽  
Finite Breadth ◽  
Quasiconvex Subgroups

We define a new invariant of a conjugacy class of subgroups which we call the breadth and prove that a quasiconvex subgroup of a negatively curved group has finite breadth in the ambient group. Utilizing the coset graph and the geodesic core of a subgroup we give an explicit algorithm for constructing a finite generating set for an intersection of a quasiconvex subgroup of a negatively curved group with its conjugate. Using that algorithm we construct algorithms for computing the breadth, the width, and the height of a quasiconvex subgroup of a negatively curved group. These algorithms decide if a quasiconvex subgroup of a negatively curved group is almost malnormal in the ambient group. We also explicitly compute a quasiconvexity constant of the intersection of two quasiconvex subgroups and give examples demonstrating that height, width, and breadth are different invariants of a subgroup.

scholarly journals Tameness and geodesic cores of subgroups

2000 ◽  
Vol 69 (2) ◽  
pp. 153-161 ◽  
Author(s):  
Rita Gitik
Keyword(s):  
Normal Subgroup ◽  
Factor Group ◽  
Finitely Generated ◽  
Finitely Generated Group ◽  
Negatively Curved ◽  
Quasiconvex Subgroups ◽  
Trivial Subgroup

AbstractLet N be a finitely generated normal subgroup of a finitely generated group G. We show that if the trivial subgroup is tame in the factor group G/N, then N is that in G. We also give a short new proof of the fact that quasiconvex subgroups of negatively curved groups are tame. The proof utilizes the concept of the geodesic core of the subgroup and is related to the Dehn algorithm.

Double-Helix Supramolecular Nanofibers Assembled from Negatively Curved Nanographenes

2021 ◽  
Author(s):  
Kenta Kato ◽  
Kiyofumi Takaba ◽  
Saori Maki-Yonekura ◽  
Nobuhiko Mitoma ◽  
Yusuke Nakanishi ◽  
...  
Keyword(s):  
Double Helix ◽  
Negatively Curved

Torus actions, maximality, and non-negative curvature

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Christine Escher ◽  
Catherine Searle
Keyword(s):  
Negative Curvature ◽  
Torus Action ◽  
Maximal Symmetry ◽  
Curved Manifolds ◽  
Negatively Curved ◽  
Product Of Spheres ◽  
Rank Conjecture ◽  
Simply Connected ◽  
Symmetry Rank ◽  
Special Case

Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we show the Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.

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