Knots, Groups, and 3-manifolds: Papers Dedicated to the Memory of R. H. Fox

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Ralph Hartzler Fox, Lee Paul Neuwirth
Princeton University Press, Aug 21, 1975 - Mathematics - 335 pages

There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends.



In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin.



Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.

 

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Contents

SYMMETRIC FIBERED LINKS
3
KNOT MODULES
25
THE THIRD HOMOTOPY GROUP OF SOME HIGHER DIMENSIONAL KNOTS
35
OCTAHEDRAL KNOT COVERS
47
SOME KNOTS SPANNED BY MORE THAN ONE UNKNOTTED SURFACE OF MINIMAL GENUS
51
GROUPS AND MANIFOLDS CHARACTERIZING LINKS
63
Group Theory
85
HNN GROUPS AND GROUPS WITH CENTER
87
KNOTLIKE GROUPS
119
3Dimensional Manifolds
135
ON THE EQUIVALENCE OF HEEGAARD SPLITTINGS OF CLOSED ORIENTABLE 3MANIFOLDS
137
BRANCHED CYCLIC COVERINGS
165
ON THE 3DIMENSIONAL BRIESKORN MANIFOLDS Mpqr
175
SURGERY ON LINKS AND DOUBLE BRANCHED COVERS OF Sł
227
PLANAR REGULAR COVERINGS OF ORIENTABLE CLOSED SURFACES
261
INFINITELY DIVISIBLE ELEMENTS IN 3MANIFOLD GROUPS
293

QUOTIENTS OF THE POWERS OF THE AUGMENTATION IDEAL IN A GROUP RING
101

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