Dual Decompositions of 4-manifolds Ii: Linear Link Invariants
نویسندگان
چکیده
This paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index ≤ 2. Part I gave existence results in terms of spines and chain complexes over the fundamental group of the ambient manifold. Here we exploit the fact that one side of a decomposition frequently has larger fundamental group to define algebraic-topological invariants. The main theorems are realization results for these invariants. This reveals a basic asymmetry in these decompositions: subtle changes on one side can force algebraic-topologically detectable changes on the other. The connection to link invariants comes through thinking of the “subtle” side as determined by the link used as attaching maps for its 2-handles. A solvable iteration of the basic invariant gives an “obstruction theory” related to the Cochran-Orr-Teichner filtration of the link concordance groups, and the finite-type invariants developed following Vassilaev.
منابع مشابه
Dual Decompositions of 4-manifolds Ii: Linear Invariants
This paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index ≤ 2. Part I (Trans. Amer. Math. Soc. 354 (2002), 1373–1392) gave existence results in terms of spines and chain complexes over the fundamental group of the ambient manifold. Here we assume that one side of a decomposition has larger fundamental group, and use this to define algebr...
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