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Some hyperbolic space forms with few generated fundamental groups

Alberto Cavicchioli|Emil Molnar|Agnese I. Telloni
대한수학회 (The Korean Mathematical Society)|2013.03|대한수학회지 (Journal of the KMS)|제50권 제2호|pp. 425-444

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참고문헌

키워드

fundamental groupcyclic branched coveringHeegaard diagramisometry grouphyperbolic 3--manifoldhyperelliptic involutionhyperbolic orbifold
주제분류수학

초록

We construct some hyperbolic hyperelliptic space forms wh-ose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extendedCoxeter group generated by plane reections and half-turns. Then wedescribe covering properties and determine the isometry groups of theconstructed manifolds. Furthermore, we give an explicit construction ofspace form of the second smallest volume nonorientable hyperbolic 3{manifold with one cusp.

Abstract

We construct some hyperbolic hyperelliptic space forms wh-ose fundamental groups are generated by only two or three isometries. Each occurring group is obtained from a supergroup, which is an extendedCoxeter group generated by plane reections and half-turns. Then wedescribe covering properties and determine the isometry groups of theconstructed manifolds. Furthermore, we give an explicit construction ofspace form of the second smallest volume nonorientable hyperbolic 3{manifold with one cusp.

참고문헌 (26)

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