2019
DOI: 10.5802/aif.3245
|View full text |Cite
|
Sign up to set email alerts
|

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

Abstract: 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 a… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
1
1

Citation Types

2
19
0

Year Published

2019
2019
2024
2024

Publication Types

Select...
5

Relationship

2
3

Authors

Journals

citations
Cited by 9 publications
(21 citation statements)
references
References 10 publications
2
19
0
Order By: Relevance
“…The first examples of Kähler groups with exotic finiteness properties were constructed by Dimca, Papadima and Suciu in [21] by considering a particular map from a product of hyperbolic surfaces to an elliptic curve. The following construction of the second author [27] extends their result to a much wider class of maps.…”
Section: If F Factors Asmentioning
confidence: 74%
See 2 more Smart Citations
“…The first examples of Kähler groups with exotic finiteness properties were constructed by Dimca, Papadima and Suciu in [21] by considering a particular map from a product of hyperbolic surfaces to an elliptic curve. The following construction of the second author [27] extends their result to a much wider class of maps.…”
Section: If F Factors Asmentioning
confidence: 74%
“…This breakthrough was achieved by Dimca, Papadima and Suciu [21]. Further examples were constructed by Biswas, Mj and Pancholi [9] and by Llosa Isenrich [27]. Our main purpose here is to construct examples of a different kind.…”
Section: Introductionmentioning
confidence: 99%
See 1 more Smart Citation
“…This possibility was already discussed in [9,11], and put into use in [48]. We also mention here that there exist Kähler groups which are subgroups of direct products of surface groups but which are not of type FP ∞ , see [25,43].…”
Section: Cubulable Kähler Manifolds and Groups 41 Cubulable Kähler Gmentioning
confidence: 84%
“…In recent work the author of this paper generalised Dimca, Papadima and Suciu's construction [10] and the techniques used here give explicit finite presentations for many of the resulting groups.…”
Section: Introductionmentioning
confidence: 99%