6533b821fe1ef96bd127af3b
RESEARCH PRODUCT
On cyclic branched coverings of prime knots
Michel BoileauLuisa Paoluzzisubject
[ MATH.MATH-GT ] Mathematics [math]/Geometric Topology [math.GT]Primary 57M25010102 general mathematicsGeometric Topology (math.GT)01 natural sciencesMathematics::Geometric Topology57M25 (57M12 57M50)57M50CombinatoricsMathematics - Geometric TopologyKnot (unit)Prime knot[MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT]0103 physical sciencesHomogeneous spaceSecondary 57M12FOS: MathematicsPrimary 57M25; Secondary 57M12; 57M50010307 mathematical physicsGeometry and Topology0101 mathematicsComputingMilieux_MISCELLANEOUS[MATH.MATH-GT] Mathematics [math]/Geometric Topology [math.GT]Mathematicsdescription
We prove that a prime knot K is not determined by its p-fold cyclic branched cover for at most two odd primes p. Moreover, we show that for a given odd prime p, the p-fold cyclic branched cover of a prime knot K is the p-fold cyclic branched cover of at most one more knot K' non equivalent to K. To prove the main theorem, a result concerning the symmetries of knots is also obtained. This latter result can be interpreted as a characterisation of the trivial knot.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2007-02-26 |