Geodesic
Fiber surfaces from alternating states
Girão, Darlan1 ; Nogueira, João2 ; Salgueiro, António2
1Department of Mathematics, Universidade Federal do Ceará, Av. Humberto Monte S/N, Campus do Pici – Bloco 914, 60455-760 Fortaleza-CE, Brazil
2CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal
Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2803-2815
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In this paper we define alternating Kauffman states of links and we characterize when the induced state surface is a fiber. In addition, we give a different proof of a similar theorem of Futer, Kalfagianni and Purcell on homogeneous states.

DOI : 10.2140/agt.2015.15.2805
Classification : 57M25, 57M15
Keywords: fibered links, state surfaces

Girão, Darlan  1   ; Nogueira, João  2   ; Salgueiro, António  2

1 Department of Mathematics, Universidade Federal do Ceará, Av. Humberto Monte S/N, Campus do Pici – Bloco 914, 60455-760 Fortaleza-CE, Brazil
2 CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Santa Cruz, 3001-501 Coimbra, Portugal 
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Girão, Darlan; Nogueira, João; Salgueiro, António. Fiber surfaces from alternating states. Algebraic and Geometric Topology, Tome 15 (2015) no. 5, pp. 2803-2815. doi: 10.2140/agt.2015.15.2805

[1] D Futer, Fiber detection for state surfaces, Algebr. Geom. Topol. 13 (2013) 2799

[2] D Futer, E Kalfagianni, J Purcell, Guts of surfaces and the colored Jones polynomial, Lecture Notes in Mathematics 2069, Springer (2013)

[3] D Gabai, Detecting fibred links in $S^3$, Comment. Math. Helv. 61 (1986) 519

[4] D Girão, On the fibration of augmented link complements, Geom. Dedicata 168 (2014) 207

[5] S Goodman, G Tavares, Pretzel-fibered links, Bol. Soc. Brasil. Mat. 15 (1984) 85

[6] J Harer, How to construct all fibered knots and links, Topology 21 (1982) 263

[7] K Murasugi, On a certain subgroup of the group of an alternating link, Amer. J. Math. 85 (1963) 544

[8] J R Stallings, Constructions of fibred knots and links, from: "Algebraic and geometric topology, Part 2" (editor R J Milgram), Proc. Sympos. Pure Math. 32, Amer. Math. Soc. (1978) 55

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