Embedding spheres in knot traces
| Autor: | Mark Powell, Allison N. Miller, Arunima Ray, Peter Feller, Matthias Nagel, Patrick Orson |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Homotopy group Fundamental group Algebra and Number Theory 010308 nuclear & particles physics Homotopy 010102 general mathematics Geometric Topology (math.GT) Alexander polynomial 01 natural sciences Mathematics::Algebraic Topology Mathematics::Geometric Topology Manifold Mathematics - Geometric Topology Arf invariant 0103 physical sciences FOS: Mathematics 0101 mathematics Abelian group Knot (mathematics) Mathematics 57K40 57K10 57N35 57N70 57R67 |
| Zdroj: | Compositio Mathematica Compositio Mathematica, 2021, Vol.157(10), pp.2242-2279 [Peer Reviewed Journal] Compositio Mathematica, 157 (10) |
| ISSN: | 0010-437X 1570-5846 |
| Popis: | The trace of the -framed surgery on a knot in is a 4-manifold homotopy equivalent to the 2-sphere. We characterise when a generator of the second homotopy group of such a manifold can be realised by a locally flat embedded -sphere whose complement has abelian fundamental group. Our characterisation is in terms of classical and computable -dimensional knot invariants. For each, this provides conditions that imply a knot is topologically -shake slice, directly analogous to the result of Freedman and Quinn that a knot with trivial Alexander polynomial is topologically slice. Compositio Mathematica, 157 (10) ISSN:0010-437X ISSN:1570-5846 |
| Databáze: | OpenAIRE |
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