Finite presentations for Kähler groups with arbitrary finiteness properties

Isenrich, Claudio Llosa

doi:10.1016/j.jalgebra.2016.12.011

Cited by 5 publications

(6 citation statements)

References 12 publications

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“…Remark 3.7. Under the additional condition that the maps f i ∶ Λ i → Z k are surjective all groups that arise in this way are group theoretic fibre products over Z k ; one can construct explicit finite presentations for them using the same methods as in [11].…”

Section: A Kähler Analogue Of Bestvina-brady Groupsmentioning

confidence: 99%

“…By looking at a suitable concrete realisation of the map f g (see [11] for more details), it is not hard to see that it induces the map…”

Section: Constructing a Bestvina-brady Type Class Of Examplesmentioning

confidence: 99%

“…The construction given by Dimca, Papadima and Suciu is a topological construction and does not lead to an explicit finite presentation. In [11], Llosa Isenrich derived an explicit presentation for these examples, answering a question of Suciu. The original proof that Dimca, Papadima and Suciu's examples have arbitrary finiteness properties consists of an involved argument making use of characteristic varieties.…”

Section: Introductionmentioning

confidence: 97%

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Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

Isenrich¹

2019

Annales De l'Institut Fourier

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We construct Kähler groups with arbitrary finiteness properties by mapping products of closed Riemann surfaces holomorphically onto an elliptic curve: for each r ≥ 3, we obtain large classes of Kähler groups that have classifying spaces with finite (r − 1)-skeleton but do not have classifying spaces with finitely many r-cells. We describe invariants which distinguish many of these groups. Our construction is inspired by examples of Dimca, Papadima and Suciu.Under the additional assumption that all maps f g i are purely branched, we will give the following complete classification of all Kähler groups that can be obtained using our construction.

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Section: A Kähler Analogue Of Bestvina-brady Groupsmentioning

confidence: 99%

“…By looking at a suitable concrete realisation of the map f g (see [11] for more details), it is not hard to see that it induces the map…”

Section: Constructing a Bestvina-brady Type Class Of Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

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Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

Isenrich¹

2019

Annales De l'Institut Fourier

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“…Therefore, given finite presentations for the groups π 1 X N i ,m , 1 ≤ i ≤ r, we could apply an algorithm developed by the first author, Howie, Miller and Short [12] to construct explicit finite presentations for our examples. An implementation by the second author in a similar situation [28] demonstrates the practical nature of this algorithm.…”

Section: Construction Of Kähler Groupsmentioning

confidence: 89%

Kodaira fibrations, Kähler groups, and finiteness properties

Bridson

Isenrich

2019

Trans. Amer. Math. Soc.

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“…For (1), it would be necessary to implement a special case of the Effective 1-2-3 Theorem from [6] -cf. [15].…”

Section: Connections and Challengesmentioning

confidence: 99%

Binary Subgroups of Direct Products

Bridson¹

2022

Preprint

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We explore an elementary construction that produces finitely presented groups with diverse homological finiteness properties -the binary subgroups,These full subdirect products require strikingly few generators. If each G i is finitely presented, B(Σ, µ) is finitely presented. When the G i are non-abelian limit groups (e.g. free or surface groups), the B(Σ, µ) provide new examples of finitely presented, residually-free groups that do not have finite classifying spaces but are not of Stallings-Bieri type. We answer a question of Minasyan relating different notions of rank for residually-free groups. And we prove that if G 1 , . . . , G m are perfect groups, each requiring at most r generators, then G 1 × • • •× G m requires at most r⌊log 2 m + 1⌋ generators.

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Finite presentations for Kähler groups with arbitrary finiteness properties

Abstract: We construct the first explicit finite presentations for a family of Kähler groups with arbitrary finiteness properties, answering a question of Suciu.

Cited by 5 publications

References 12 publications

Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

Branched covers of elliptic curves and Kähler groups with exotic finiteness properties

Kodaira fibrations, Kähler groups, and finiteness properties

Binary Subgroups of Direct Products

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