On polynomials and surfaces of variously positive links

Stoimenow, Alexander. "On polynomials and surfaces of variously positive links." Journal of the European Mathematical Society 007.4 (2005): 477-509. <http://eudml.org/doc/277349>.

@article{Stoimenow2005,
abstract = {It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is 1, with a similar relation for links. We extend this result to almost positive links and partly identify the next three coefficients for special types of positive links. We also give counterexamples to the Jones polynomial-ribbon genus conjectures for a quasipositive knot. Then we show that the Alexander polynomial completely detects the minimal genus and fiber property of canonical Seifert surfaces associated to almost positive (and almost alternating) link diagrams.},
author = {Stoimenow, Alexander},
journal = {Journal of the European Mathematical Society},
keywords = {positive link; quasipositive link; almost positive link; almost alternating link; Alexander polynomial; Jones polynomial; fiber surface; ribbon genus; positive link; quasipositive link; almost positive link; almost alternating link; Alexander polynomial; Jones polynomial; fiber surface; ribbon genus},
language = {eng},
number = {4},
pages = {477-509},
publisher = {European Mathematical Society Publishing House},
title = {On polynomials and surfaces of variously positive links},
url = {http://eudml.org/doc/277349},
volume = {007},
year = {2005},
}

TY - JOUR
AU - Stoimenow, Alexander
TI - On polynomials and surfaces of variously positive links
JO - Journal of the European Mathematical Society
PY - 2005
PB - European Mathematical Society Publishing House
VL - 007
IS - 4
SP - 477
EP - 509
AB - It is known that the minimal degree of the Jones polynomial of a positive knot is equal to its genus, and the minimal coefficient is 1, with a similar relation for links. We extend this result to almost positive links and partly identify the next three coefficients for special types of positive links. We also give counterexamples to the Jones polynomial-ribbon genus conjectures for a quasipositive knot. Then we show that the Alexander polynomial completely detects the minimal genus and fiber property of canonical Seifert surfaces associated to almost positive (and almost alternating) link diagrams.
LA - eng
KW - positive link; quasipositive link; almost positive link; almost alternating link; Alexander polynomial; Jones polynomial; fiber surface; ribbon genus; positive link; quasipositive link; almost positive link; almost alternating link; Alexander polynomial; Jones polynomial; fiber surface; ribbon genus
UR - http://eudml.org/doc/277349
ER -