TY - JOUR
T1 - Essential twisted surfaces in alternating link complements
AU - Lackenby, Marc
AU - Purcell, Jessica
PY - 2016/12/15
Y1 - 2016/12/15
N2 - Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement.
AB - Checkerboard surfaces in alternating link complements are used frequently to determine information about the link. However, when many crossings are added to a single twist region of a link diagram, the geometry of the link complement stabilizes (approaches a geometric limit), but a corresponding checkerboard surface increases in complexity with crossing number. In this paper, we generalize checkerboard surfaces to certain immersed surfaces, called twisted checkerboard surfaces, whose geometry better reflects that of the alternating link in many cases. We describe the surfaces, show that they are essential in the complement of an alternating link, and discuss their properties, including an analysis of homotopy classes of arcs on the surfaces in the link complement.
KW - alternating links
KW - essential surfaces
UR - http://www.scopus.com/inward/record.url?scp=85007009701&partnerID=8YFLogxK
U2 - 10.2140/agt.2016.16.3209
DO - 10.2140/agt.2016.16.3209
M3 - Article
AN - SCOPUS:85007009701
VL - 16
SP - 3209
EP - 3270
JO - Algebraic & Geometric Topology
JF - Algebraic & Geometric Topology
SN - 1472-2747
IS - 6
ER -