Cube complexes, subgroups of mapping class
                    groups, and nilpotent genus

Bridson, Martin R.

doi:10.1090/pcms/021/11

Cited by 4 publications

(2 citation statements)

References 59 publications

(88 reference statements)

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“…The first steps in our construction of the triples M ãÑ P ãÑ Γ in Theorem A follow the template for constructing finitely presented Grothendieck pairs that originates in [10] and is explicit in Section 8 of [7]. We craft finitely presented groups Q that enjoy an array of properties relevant to our aims (Section 3.1); we use a suitably-adapted form of the Rips construction (Proposition 3.1) to produce short exact sequences 1 Ñ N Ñ G Ñ Q Ñ 1 with G finitely presented and residually finite, N finitely generated, and both N and G perfect; and we take a fibre product of several copies of G Ñ Q to produce N d ãÑ P d ãÑ G d with P d finitely presented.…”

Section: Theorem B If a Is A Finitely Generated Group With Finite Abe...mentioning

confidence: 99%

Profinite Rigidity, Fibering, and the Figure-Eight Knot

Bridson¹,

Reid²

2019

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We describe a flexible construction that produces triples of finitely generated, residually finite groups M ãÑ P ãÑ Γ, where the maps induce isomorphisms of profinite completions x M -p P -p Γ, but M and Γ have Serre's property FA while P does not. In this construction, P is finitely presented and Γ is of type F8. More generally, given any positive integer d, one can demand that M and Γ have a fixed point whenever they act by semisimple isometries on a complete CATp0q space of dimension at most d, while P acts without a fixed point on a tree.

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Section: Theorem B If a Is A Finitely Generated Group With Finite Abe...mentioning

confidence: 99%

Profinite Rigidity, Fibering, and the Figure-Eight Knot

Bridson¹,

Reid²

2019

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“…Martin Bridson has proved [23] that there exist families of right-angled Artin groups for which this problem is unsolvable, even for finitely presented subgroups. Let us briefly recall the construction.…”

Section: Subgroup Isomorphism Problem and Proposed Authentication Schmentioning

confidence: 99%

Cryptography with right-angled Artin groups

Flores

Kahrobaei

2017

Theor. Appl. Inform.

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In this paper we propose right-angled Artin groups as a platform for secret sharing schemes based on the efficiency (linear time) of the word problem. Inspired by previous work of Grigoriev-Shpilrain in the context of graphs, we define two new problems: Subgroup Isomorphism Problem and Group Homomorphism Problem. Based on them, we also propose two new authentication schemes. For right-angled Artin groups, the Group Homomorphism and Graph Homomorphism problems are equivalent, and the later is known to be NP-complete. In the case of the Subgroup Isomorphism problem, we bring some results due to Bridson who shows there are right-angled Artin groups in which this problem is unsolvable.

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A counterexample to Thiagarajan's conjecture on regular event structures

Chalopin

Chepoi

2020

Journal of Computer and System Sciences

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We provide a counterexample to a conjecture by Thiagarajan (1996 and 2002) that regular prime event structures correspond exactly to those obtained as unfoldings of finite 1-safe Petri nets. The same counterexample is used to disprove a closely related conjecture by Badouel, Darondeau, and Raoult (1999) that domains of regular event structures with bounded-cliques are recognizable by finite trace automata. Event structures, trace automata, and Petri nets are fundamental models in concurrency theory. There exist nice interpretations of these structures as combinatorial and geometric objects and both conjectures can be reformulated in this framework. Namely, the domains of prime event structures correspond exactly to pointed median graphs; from a geometric point of view, these domains are in bijection with pointed CAT(0) cube complexes. A necessary condition for both conjectures to be true is that domains of respective regular event structures admit a regular nice labeling. To disprove these conjectures, we describe a regular event domain (with bounded-cliques) that does not admit a regular nice labeling. Our counterexample is derived from an example by Wise (1996 and 2007) of a nonpositively curved square complex X whose universal cover X is a CAT(0) square complex containing a particular plane with an aperiodic tiling.

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Cube complexes, subgroups of mapping class groups, and nilpotent genus

Cited by 4 publications

References 59 publications

Profinite Rigidity, Fibering, and the Figure-Eight Knot

Profinite Rigidity, Fibering, and the Figure-Eight Knot

Cryptography with right-angled Artin groups

A counterexample to Thiagarajan's conjecture on regular event structures

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