Dual decompositions of 4-manifolds II: linear invariants
| dc.creator | Quinn, Frank | |
| dc.date | 2001-09-20 | |
| dc.date | 2004-03-06 | |
| dc.date.accessioned | 2026-07-07T04:43:28Z | |
| dc.date.available | 2026-07-07T04:43:28Z | |
| dc.description | This 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.description | 21 pages, 4 figures. Revised March 2004 to correct misprints and respond to referee suggestions. Still no worked-out examples, though | |
| dc.identifier | https://arxiv.org/abs/math/0109148 | |
| dc.identifier | http://arxiv.org/abs/math/0109148 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62237 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57R65 57M25 | |
| dc.title | Dual decompositions of 4-manifolds II: linear invariants | |
| dc.type | text |