A second order algebraic knot concordance group

Details A second order algebraic knot concordance group A second order algebraic knot concordance group

2012-03-20

arxiv.org/abs/1203.5645v1

Mathematics

Geometric Topology

51 pages, 2 figures. This a considerably shortened version of arXiv:1109.0761, to appear in Algebraic and Geometric Topology

Scientific paper

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.

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