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Article overview
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New topologically slice knots | Stefan Friedl
; Peter Teichner
; | Date: |
12 May 2005 | Subject: | Geometric Topology MSC-class: 57M25 | math.GT | Abstract: | In the early 1980’s Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group $$). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficient {em homological} condition under which a knot is slice with fundamental group $sr$. These two fundamental groups are known to be the only {em solvable ribbon} groups. Our homological condition implies that the Alexander polynomial equals $(t-2)(t^{-1}-2)$ but also contains information about the metabelian cover of the knot complement (since there are many non-slice knots with this Alexander polynomial). | Source: | arXiv, math.GT/0505233 | Services: | Forum | Review | PDF | Favorites |
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