Open AccessLinks with no exceptional surgeries
Author(s) -
David Futer,
Jessica S. Purcell
Publication year - 2007
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.4171/cmh/105
Subject(s) - twist , mathematics , knot (papermaking) , combinatorics , link (geometry) , crossing number (knot theory) , statement (logic) , prime (order theory) , pure mathematics , geometry , chemical engineering , political science , law , engineering
We show that if a knot admits a prime, twist-reduced diagram with at least 4twist regions and at least 6 crossings per twist region, then every non-trivialDehn filling of that knot is hyperbolike. A similar statement holds for links.We prove this using two arguments, one geometric and one combinatorial. Thecombinatorial argument further implies that every link with at least 2 twistregions and at least 6 crossings per twist region is hyperbolic and gives alower bound for the genus of a link.Comment: 28 pages, 15 figures. Minor rewording and organizational changes; also added theorem giving a lower bound on the genus of these link
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom