Link groups and the A-B slice problem

Details Link groups and the A-B slice problem Link groups and the A-B slice problem

2006-02-06

arxiv.org/abs/math/0602105v2

Topology and physics, 220-235, Nankai Tracts Math., 12, World Sci. Publ., Hackensack, NJ, 2008

Mathematics

Geometric Topology

16 pages; final version

Scientific paper

The A-B slice problem is a reformulation of the topological 4-dimensional surgery conjecture in terms of decompositions of the 4-ball and link homotopy. We show that link groups, a recently developed invariant of 4-manifolds, provide an obstruction for the class of model decompositions, introduced by M. Freedman and X.-S. Lin. This unifies and extends the previously known partial obstructions in the A-B slice program. As a consequence, link groups satisfy Alexander duality when restricted to the class of model decompositions, but not for general submanifolds of the 4-ball.

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