منابع مشابه
Knot Concordance
We prove the nontriviality at all levels of the filtration of the classical topological knot concordance group C · · · ⊆ Fn ⊆ · · · ⊆ F1 ⊆ F0 ⊆ C. defined in [COT]. This filtration is significant because not only is it strongly connected to Whitney tower constructions of Casson and Freedman, but all previously-known concordance invariants are related to the first few terms in the filtration. In...
متن کاملKnot Concordance and Torsion
The classical knot concordance group, C1, was defined in 1961 by Fox [F]. He proved that it is nontrivial by finding elements of order two; details were presented in [FM]. Since then one of the most vexing questions concerning the concordance group has been whether it contains elements of finite order other than 2–torsion. Interest in this question was heightened by Levine’s proof [L1, L2] that...
متن کاملKnot Concordance, Whitney Towers and L2-signatures
We construct many examples of non-slice knots in 3-space that cannot be distinguished from slice knots by previously known invariants. Using Whitney towers in place of embedded disks, we define a geometric filtration of the 3-dimensional topological knot concordance group. As special cases of Whitney towers of height less than four, the bottom part of the filtration exhibits all classical conco...
متن کاملKnot Concordance and Von Neumann Ρ-invariants
We present new results, announced in [T], on the classical knot concordance group C. We establish the nontriviality at all levels of the (n)-solvable filtration · · · ⊆ Fn ⊆ · · · ⊆ F1 ⊆ F0 ⊆ C introduced in [COT1]. Recall that this filtration is significant due to its intimate connection to tower constructions arising in work of A. Casson and M. Freedman on the topological classification probl...
متن کاملKnot Concordance and Homology Cobordism Workshop
I will give an overview of the n-solvable filtration of the smooth knot (or string link) concordance group including the strategy and tools used to analyze it: higher-order Alexander modules, linking forms and signature defects. I will attempt to discuss what is known about this filtration, what is not known but should be knowable by present techniques; and discuss the failings of present techn...
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ژورنال
عنوان ژورنال: Journal of Topology
سال: 2018
ISSN: 1753-8416,1753-8424
DOI: 10.1112/topo.12054