The Branched Cyclic Coverings of 2 Bridge Knots and Links

Download or Read eBook The Branched Cyclic Coverings of 2 Bridge Knots and Links PDF written by Jerome Minkus and published by American Mathematical Soc.. This book was released on 1982 with total page 75 pages. Available in PDF, EPUB and Kindle.
The Branched Cyclic Coverings of 2 Bridge Knots and Links
Author :
Publisher : American Mathematical Soc.
Total Pages : 75
Release :
ISBN-10 : 9780821822555
ISBN-13 : 0821822551
Rating : 4/5 (55 Downloads)

Book Synopsis The Branched Cyclic Coverings of 2 Bridge Knots and Links by : Jerome Minkus

Book excerpt: In this paper a family of closed oriented 3 dimensional manifolds {[italic]M[subscript italic]n([italic]k,[italic]h)} is constructed by pasting together pairs of regions on the boundary of a 3 ball. The manifold [italic]M[subscript italic]n([italic]k,[italic]h) is a generalization of the lens space [italic]L([italic]n,1) and is closely related to the 2 bridge knot or link of type ([italic]k,[italic]h). While the work is basically geometrical, examination of [lowercase Greek]Pi1([italic]M[subscript italic]n([italic]k,[italic]h)) leads naturally to the study of "cyclic" presentations of groups. Abelianizing these presentations gives rise to a formula for the Alexander polynomials of 2 bridge knots and to a description of [italic]H1([italic]M[subscript italic]n([italic]k,[italic]h), [italic]Z) by means of circulant matrices whose entries are the coefficients of these polynomials.


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