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

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. 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. CONTENTS INTRODUCTION BIBLIOGRAPHY, RALPH HARTZLER FOX Knots and Links SYMMETRIC FIBERED LINKS KNOT MODULES THE THIRD HOMOTOPY GROUP OF SOME HIGHER DIMENSIONAL KNOTS OCTAHEDRAL KNOT COVERS SOME KNOTS SPANNED BY MORE THAN ONE UNKNOTTED SURFACE OF MINIMAL GENUS GROUPS AND MANIFOLDS CHARACTERIZING LINKS Group Theory HNN GROUPS AND GROUPS WITH CENTRE QUOTIENTS OF THE POWERS OF THE AUGMENTATION IDEAL IN A GROUP RING KNOT-LIKE GROUPS 3-Dimensional Manifolds ON THE EQUIVALENCE OF HEEGAARD SPLITTINGS OF CLOSED, ORIENTABLE 3-MANIFOLDS BRANCHED CYCLIC COVERINGS ON THE 3-DIMENSIONAL BRIESKORN MANIFOLDS M(p, q, r) SURGERY ON LINKS AND DOUBLE BRANCHED COVERS OF OF S^3 PLANAR REGULAR COVERINGS OF ORIENTABLE CLOSED SURFACES INFINITELY DIVISIBLE ELEMENTS IN 3-MANIFOLD GROUPS