Complexes of Groups

Corson, Jon M.

doi:10.1112/plms/s3-65.1.199

Cited by 40 publications

(39 citation statements)

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“…Sufficient conditions for the realizability of a triangle (T) were given by Jon Corson in [5] and by Stallings in [11]. Namely, these authors showed that (T) is realizable if (T) is non-spherical in a sense which we shall now review.…”

Section: Introductionmentioning

confidence: 93%

Triangles of Groups

Chermak¹

1995

Transactions of the American Mathematical Society

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Abstract.Given a certain commutative diagram of groups and monomorphisms, does there necessarily exist a group in which the given diagram is essentially a diagram of subgroups and inclusions? In general, the answer is negative, but J. Corson, and Gersten and Stallings have shown that in the case of a "nonspherical triangle" of groups the answer is positive. This paper improves on these results by weakening the non-sphericality requirement.

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Section: Introductionmentioning

confidence: 93%

Triangles of Groups

Chermak¹

1995

Transactions of the American Mathematical Society

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“…Definition 6.1 (Complex-of-spaces). [7] A (good) complex-of-spaces K over K is a CW-complex with a cellular map p : K → K satisfying the conditions as follows:…”

Section: K-connected Sum Of a Pair Of Complexesmentioning

confidence: 99%

On the structure of braid groups on complexes

Park

2017

Topology and its Applications

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Abstract. We consider the braid groups Bn(X) on finite simplicial complexes X, which are generalizations of those on both manifolds and graphs that have been studied already by many authors. We figure out the relationships between geometric decompositions for X and their effects on braid groups, and provide an algorithmic way to compute the group presentations for Bn(X) with the aid of them.As applications, we give complete criteria for both the surface embeddability and planarity for X, which are the torsion-freeness of the braid group Bn(X) and its abelianization H 1 (Bn(X)), respectively.

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“…For an essentially identical notion in the context of discrete groups but with injective maps G (∂) see [Co92] 'labeled 2-complexes of groups'.…”

Section: Definition 21mentioning

confidence: 99%