Leseprobe
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Knots, Groups and 3-Manifolds (AM-84), Volume 84
Lee Paul Neuwirth
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Naturwissenschaften, Medizin, Informatik, Technik / Mathematik
Beschreibung
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.
Kundenbewertungen
Homotopy group, Intersection theory, Equivalence class, Complex Lie group, Homomorphism, Knot polynomial, Mapping cylinder, Proportionality (mathematics), Braid group, Algebraic equation, Automorphism, Additive group, Generating set of a group, Surjective function, Fundamental group, Graded ring, Knot group, Principal ideal domain, Group theory, Coprime integers, Complex manifold, Borromean rings, Riemann surface, Meromorphic function, Automorphic form, Group ring, Double coset, Groupoid, Cohomological dimension, 3-sphere, Coset, Heegaard splitting, Theorem, Quotient space (topology), Homeomorphism, Intersection number (graph theory), Triangle group, Commutative ring, Permutation, Algebraic surface, Divisibility rule, Variable (mathematics), Symplectic matrix, Diagram (category theory), Simplicial category, Submanifold, Seifert fiber space, Bilinear form, Integer, Conjugacy class, Equation, Torus knot, Commutator subgroup, Multiplicative group, Subgroup, Dedekind domain, Homotopy, Infimum and supremum, Algebraic variety, Homology sphere, Cyclic group, Central series, Graph product, Spectral sequence, 3-manifold, Homotopy sphere, Hurewicz theorem, Mathematical induction, Poincaré conjecture, Holomorphic function