The equivalence relation of concordance on the set of links of circles in 3-space arises naturally in attempts to resolve singularities of immersed 2-spheres in a 4-dimensional manifold. In fact, certain unsolved link concordance problems are exactly the obstructions to successfully performing surgery on 4-manifolds as the higher-dimensional theory predicts.;Directed at low dimensional topologists and knot theorists, this book investigates and clarifies higher order cohomology operations (Massey products) on the complements of links. These concordance invariants are essentially equivalent to Milnor's mu-invariants, which detect whether or not the longitudes of a link lie in the nth term of the lower-central series of the fundamental group of the link complement. The author defines higher-order linking numbers, which are seen to be "pieces" of Massey products and to have more geometric content.;His investigation leads to algorithmic realization results, calculational methods, and many new examples, including the first examples with trivial mu-invariants which are not concordant to boundary links, as well as the first examples with trivial Alexander's module but non-trivial mu-invariants. There are also new connections with geometric equivalence relations and with K.Orr's homotopy invariants.
| ISBN: | 9780821824894 |
| Publication date: | 30th July 1990 |
| Author: | Tim D Cochran |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 73 pages |
| Series: | Memoirs of the American Mathematical Society |
| Genres: |
Mathematics |