Dual decompositions of 4-manifolds II: linear invariants

dc.creatorQuinn, Frank
dc.date2001-09-20
dc.date2004-03-06
dc.date.accessioned2026-07-07T04:43:28Z
dc.date.available2026-07-07T04:43:28Z
dc.descriptionThis paper continues the study of decompositions of a smooth 4-manifold into two handlebodies with handles of index $\leq2$. Part I 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 algebraic-topological invariants. These reveal a basic asymmetry in these decompositions: subtle changes on one side can force algebraic-topologically detectable changes on the other. A solvable iteration of the basic invariant gives an ``obstruction theory'' using lower commutator quotients. By thinking of a 2-handlebody as essentially determined by the links used as attaching maps for its 2-handles this theory can be thought of a giving ``ambient'' link invariants. The moves used are related to the grope cobordism of links developed by Conant-Teichner, and the Cochran-Orr-Teichner filtration of the link concordance groups. The invariants give algebraically sophisticated ``finite type'' invariants in the sense of Vassilaev.
dc.description21 pages, 4 figures. Revised March 2004 to correct misprints and respond to referee suggestions. Still no worked-out examples, though
dc.identifierhttps://arxiv.org/abs/math/0109148
dc.identifierhttp://arxiv.org/abs/math/0109148
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/62237
dc.subjectGeometric Topology
dc.subject57R65 57M25
dc.titleDual decompositions of 4-manifolds II: linear invariants
dc.typetext

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