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Dehn surgeries on some classical links

Part of: Special aspects of infinite or finite groups Low-dimensional topology Differential topology

Published online by Cambridge University Press:  19 January 2011

Alberto Cavicchioli ,
Fulvia Spaggiari  and
Agnese Ilaria Telloni
Alberto Cavicchioli
Affiliation:
Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy ([email protected]; [email protected]; [email protected])
Fulvia Spaggiari
Affiliation:
Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy ([email protected]; [email protected]; [email protected])
Agnese Ilaria Telloni
Affiliation:
Dipartimento di Matematica, Università di Modena e Reggio Emilia, Via Campi 213/B, 41100 Modena, Italy ([email protected]; [email protected]; [email protected])
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Abstract

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We consider orientable closed connected 3-manifolds obtained by performing Dehn surgery on the components of some classical links such as Borromean rings and twisted Whitehead links. We find geometric presentations of their fundamental groups and describe many of them as 2-fold branched coverings of the 3-sphere. Finally, we obtain some topological applications on the manifolds given by exceptional surgeries on hyperbolic 2-bridge knots.

Keywords

3-manifoldslinksDehn surgeryexceptional surgeriesgroup presentationscyclic branched coverings

MSC classification

Secondary: 57M12: Special coverings, e.g. branched 57R65: Surgery and handlebodies 20F05: Generators, relations, and presentations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 1 , February 2011 , pp. 33 - 45
Copyright
Copyright © Edinburgh Mathematical Society 2011

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