A second order algebraic knot concordance group
Copyright policy )A second order algebraic knot concordance group
We define an algebraic group comprising symmetric chain complexes which captures the first two stages of the Cochran-Orr-Teichner solvable filtration of the knot concordance group in a single invariant. To achieve this we impose additional structure on each chain complex which puts extra control on the fundamental groups, and in particular on the way in which they can change in a concordance.
51 pages, 2 figures. This a considerably shortened version of arXiv:1109.0761, to appear in Algebraic and Geometric Topology
- Indiana University United States
- Department of Mathematics
- University of Edinburgh United Kingdom
- DePaul University United States
concordance, knots, knot concordance group, solvable filtration, Mathematics - Geometric Topology, 57M10, geometric topology, knot, FOS: Mathematics, Knots and links in the \(3\)-sphere, 57M25, 57M27, 55U15, 57N70 (Primary), 57M05, 57M10, 57R65, 57R67, 57P10 (Secondary), abelian monoid, symmetric chain complex, single stage obstruction group, COT filtration, Geometric Topology (math.GT), 57N70, 57M27, 57R65, algebraic concordance group, 57M25, 57R67, Poincaré triad, 57M25, 57M27, 55U15, 57N70 (Primary) 57M05, 57M10, 57R65, 57R67, 57P10 (Secondary)
concordance, knots, knot concordance group, solvable filtration, Mathematics - Geometric Topology, 57M10, geometric topology, knot, FOS: Mathematics, Knots and links in the \(3\)-sphere, 57M25, 57M27, 55U15, 57N70 (Primary), 57M05, 57M10, 57R65, 57R67, 57P10 (Secondary), abelian monoid, symmetric chain complex, single stage obstruction group, COT filtration, Geometric Topology (math.GT), 57N70, 57M27, 57R65, algebraic concordance group, 57M25, 57R67, Poincaré triad, 57M25, 57M27, 55U15, 57N70 (Primary) 57M05, 57M10, 57R65, 57R67, 57P10 (Secondary)
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