Link groups of 4-manifolds

Details Link groups of 4-manifolds Link groups of 4-manifolds

2005-10-24

arxiv.org/abs/math/0510507v3

Mathematics

Geometric Topology

34 pages, 7 figures. v.3: minor phrasing changes

Scientific paper

The notion of a Bing cell is introduced, and it is used to define invariants, link groups, of 4-manifolds. Bing cells combine some features of both surfaces and 4-dimensional handlebodies, and the link group \lambda(M) measures certain aspects of the handle structure of a 4-manifold M. This group is a quotient of the fundamental group, and examples of manifolds are given with \pi_1(M) not equal to \lambda(M). The main construction of the paper is a generalization of the Milnor group, which is used to formulate an obstruction to embeddability of Bing cells into 4-space. Applications to the A-B slice problem and to the structure of topological arbiters are discussed.

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