Geodesic
Essential twisted surfaces in alternating link complements
Lackenby, Marc1 ; Purcell, Jessica2
1Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
2School of Mathematical Sciences, Monash University, 9 Rainforest Walk, Room 401, Monash University VIC 3800, Australia
Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3209-3270
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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.

DOI : 10.2140/agt.2016.16.3209
Classification : 57M25
Keywords: alternating links, essential surfaces

Lackenby, Marc  1   ; Purcell, Jessica  2

1 Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, United Kingdom
2 School of Mathematical Sciences, Monash University, 9 Rainforest Walk, Room 401, Monash University VIC 3800, Australia 
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Lackenby, Marc; Purcell, Jessica. Essential twisted surfaces in alternating link complements. Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3209-3270. doi: 10.2140/agt.2016.16.3209

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