Knots, Groups and 3-Manifolds (AM-84), Volume 84: Papers Dedicated to the Memory of R.H. Fox. (AM-84)

Lee Paul Neuwirth

Published by Princeton University Press 1975

Knots, Groups and 3-Manifolds (AM-84), Volume 84

Papers Dedicated to the Memory of R.H. Fox. (AM-84)

Lee Paul Neuwirth

Volume 84 in the series Annals of Mathematics Studies

https://doi.org/10.1515/9781400881512

Overview
Contents

About this book

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.

Topics

Frontmatter Publicly Available Download PDF	i
CONTENTS Publicly Available Download PDF	v
INTRODUCTION L. Neuwirth Requires Authentication Unlicensed Licensed Download PDF	vii
BIBLIOGRAPHY, RALPH HARTZLER FOX (1913-1973) Requires Authentication Unlicensed Licensed Download PDF	viii
Knots and Links
SYMMETRIC FIBERED LINKS Deborah L. Goldsmith Requires Authentication Unlicensed Licensed Download PDF	3
KNOT MODULES Jerome Levine Requires Authentication Unlicensed Licensed Download PDF	25
THE THIRD HOMOTOPY GROUP OF SOME HIGHER DIMENSIONAL KNOTS S. J . Lomonaco Requires Authentication Unlicensed Licensed Download PDF	35
OCTAHEDRAL KNOT COVERS Kenneth A. Perko Requires Authentication Unlicensed Licensed Download PDF	47
SOME KNOTS SPANNED BY MORE THAN ONE UNKNOTTED SURFACE OF MINIMAL GENUS H. F . Trotter Requires Authentication Unlicensed Licensed Download PDF	51
GROUPS AND MANIFOLDS CHARACTERIZING LINKS Wilbur Whitten Requires Authentication Unlicensed Licensed Download PDF	63
Group Theory
HNN GROUPS AND GROUPS WITH CENTER John Cossey and N. Smythe Requires Authentication Unlicensed Licensed Download PDF	87
QUOTIENTS OF THE POWERS OF THE AUGMENTATION IDEAL IN A GROUP RING John R. Stallings Requires Authentication Unlicensed Licensed Download PDF	101
KNOT-LIKE GROUPS Elvira Rapaport Strasser Requires Authentication Unlicensed Licensed Download PDF	119
3-Dimensional Manifolds
ON THE EQUIVALENCE OF HEEGAARD SPLITTINGS OF CLOSED, ORIENT ABLE 3-MANIFOLDS Joan S. Birman Requires Authentication Unlicensed Licensed Download PDF	137
BRANCHED CYCLIC COVERINGS Sylvain E. Cappell and Julius L. Shaneson Requires Authentication Unlicensed Licensed Download PDF	165
ON THE 3-DIMENSIONAL BRIESKORN MANIFOLDS M(p,q,r) John Milnor Requires Authentication Unlicensed Licensed Download PDF	175
SURGERY ON LINKS AND DOUBLE BRANCHED COVERS OF S³ Jose M. Montesinos Requires Authentication Unlicensed Licensed Download PDF	227
PLANAR REGULAR COVERINGS OF ORIENTABLE CLOSED SURFACES C. D. Papakyriakopoulos Requires Authentication Unlicensed Licensed Download PDF	261
INFINITELY DIVISIBLE ELEMENTS IN 3-MANIFOLD GROUPS Peter B. Shalen Requires Authentication Unlicensed Licensed Download PDF	293
Backmatter Requires Authentication Unlicensed Licensed Download PDF	337