6533b7dbfe1ef96bd1270d2f
RESEARCH PRODUCT
Three cyclic branched covers suffice to determine hyperbolic knots.
Luisa Paoluzzisubject
Discrete mathematics[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Quantitative Biology::BiomoleculesAlgebra and Number TheoryCoprime integers010102 general mathematics01 natural sciencesMathematics::Geometric TopologyCombinatoricsKnot (unit)[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciences010307 mathematical physics0101 mathematics[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematicsdescription
Let n > m > 2 be two fixed coprime integers. We prove that two Conway reducible, hyperbolic knots sharing the 2-fold, m-fold and n-fold cyclic branched covers are equivalent. Using previous results by Zimmermann we prove that this implies that a hyperbolic knot is determined by any three of its cyclic branched covers.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-08-01 |