Pretzel knots

In knot theory , a branch of mathematics , pretzel knots are a class of knots.

definition

The (-2,3,7) pretzel knot has 2 right-handed twists in the first tangle, 3 left-handed twists in the second tangle, 7 left-handed twists in the third tangle.

Be whole numbers. The - pretzel link is selected from Tangles existing entanglement whose -th Tangle from (depending on the sign of is right- or left-handed) twists. ${\displaystyle p_{1},\ldots ,p_{n}}$ ${\displaystyle (p_{1},\ldots ,p_{n})}$ ${\displaystyle n}$ ${\displaystyle i}$ ${\displaystyle \mid p_{i}\mid }$ ${\displaystyle p_{i}}$

If the loop is contiguous , it is the - pretzel knot . ${\displaystyle (p_{1},\ldots ,p_{n})}$

literature

• Gerhard Burde, Heiner Zieschang: Knots. Second edition. de Gruyter Studies in Mathematics, 5.Walter de Gruyter & Co., Berlin 2003, ISBN 3-11-017005-1 , xii + 559 pp.