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2-TORSION IN THE n-SOLVABLE FILTRATION OF THE KNOT CONCORDANCE GROUP
| Content Provider | Semantic Scholar |
|---|---|
| Author | Cochran, T. Harvey, Shelly L. Leidy, Constance |
| Copyright Year | 2009 |
| Abstract | Cochran-Orr-Teichner introduced in [11] a natural filtration of the smooth knot concordance group C · · · ⊂ Fn+1 ⊂ Fn.5 ⊂ Fn ⊂ · · · ⊂ F1 ⊂ F0.5 ⊂ F0 ⊂ C, called the (n)-solvable filtration. We show that each associated graded abelian group {Gn = Fn/Fn.5 | n ∈ N}, n ≥ 2 contains infinite linearly independent sets of elements of order 2 (this was known previously for n = 0, 1). Each of the representative knots is negative amphichiral, with vanishing s-invariant, τ -invariant, δ-invariants and Casson-Gordon invariants. Moreover each is slice in a rational homology 4-ball. In fact we show that there are many distinct such classes in Gn, one for each “distinct” n-tuple P = (p1(t), ..., pn(t)) of knot polynomials. Such a sequence of polynomials records the orders of certain submodules of a sequence of higher-order Alexander modules of the knot. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/0907.4789v1.pdf |
| Alternate Webpage(s) | http://cleidy.web.wesleyan.edu/research/2011LMS.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Class Concordance (publishing) Fibronectin Type III Domain Homology (biology) Knot (unit) Knot polynomial Stochastic process Warnier/Orr diagram filtration |
| Content Type | Text |
| Resource Type | Article |
