Combinatorial Seifert fibred spaces with transitive cyclic automorphism group

Burton, Benjamin and Spreer, Jonathan (2016) Combinatorial Seifert fibred spaces with transitive cyclic automorphism group. Israel Journal of Mathematics, 214 2: 741-784. doi:10.1007/s11856-016-1330-9

Author Burton, Benjamin
Spreer, Jonathan
Title Combinatorial Seifert fibred spaces with transitive cyclic automorphism group
Journal name Israel Journal of Mathematics   Check publisher's open access policy
ISSN 1565-8511
Publication date 2016-07-01
Year available 2016
Sub-type Article (original research)
DOI 10.1007/s11856-016-1330-9
Open Access Status Not yet assessed
Volume 214
Issue 2
Start page 741
End page 784
Total pages 44
Place of publication Jerusalem, Israel
Publisher Magnes Press
Language eng
Formatted abstract
In combinatorial topology we aim to triangulate manifolds such that their topological properties are reflected in the combinatorial structure of their description. Here, we give a combinatorial criterion on when exactly triangulations of 3-manifolds with transitive cyclic symmetry can be generalised to an infinite family of such triangulations with similarly strong combinatorial properties.

In particular, we construct triangulations of Seifert fibred spaces with transitive cyclic symmetry where the symmetry preserves the fibres and acts non-trivially on the homology of the spaces. The triangulations include the Brieskorn homology spheres Σ(p, q, r), the lens spaces L(q, 1) and, as a limit case, (S2 × S1)#(p-1)(q-1).
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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