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This textbook contains ideas and problems involving curves, surfaces, and knots, which make up the core of topology. Carlson (mathematics, Rose-Hulman Institute of Technology) introduces some basic ideas and problems concerning manifolds, especially one- and two- dimensional man…
This paper is concerned with the spectral theory of the Laplacian as the underlying Riemann surface is "pinched down" to a surface with nodes. The problem is attacked from the (general) standpoint of regular b-groups and the Selberg trace formula.
The author studies the group of rational concordance classes of codimension two knots in rational homology spheres. He gives a full calculation of its algebraic theory by developing a complete set of new invariants. For computation, he relates these invariants with limiting beha…
A knot K is said to have Property P if simply-connected 3-manifolds cannot be obtained by non-trivial Dehn surgeries along K. Torus knots, twist knots, a class of 2-bridge knots, and 2-bridge knots with 9 or fewer crossings are known to have Property P. On the other hand, Ochiai…
The group of concordance classes of high dimensional homotopy spheres knotted in codimension two in the standard sphere has an intricate algebraic structure which this paper unravels. The first level of invariants is given by the classical Alexander polynomial. By means of a tra…
The author considers the set [italic]G[italic subscript]n[italic superscript]t([italic]M) (where [italic]M is a manifold) of embeddings of [italic]S[italic superscript]n × [italic]M in [italic]S[italic superscript]n+[italic superscript]2 × [italic]M, homotopic (relative to the b…
