Estimating the states of the Kauffman bracket skein module
Bullock, Doug
Banach Center Publications, Tome 43 (1998), p. 23-28 / Harvested from The Polish Digital Mathematics Library

The states of the title are a set of knot types which suffice to create a generating set for the Kauffman bracket skein module of a manifold. The minimum number of states is a topological invariant, but quite difficult to compute. In this paper we show that a set of states determines a generating set for the ring of SL2(C) characters of the fundamental group, which in turn provides estimates of the invariant.

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:208809
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     author = {Bullock, Doug},
     title = {Estimating the states of the Kauffman bracket skein module},
     journal = {Banach Center Publications},
     volume = {43},
     year = {1998},
     pages = {23-28},
     zbl = {0902.57016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p23bwm}
}
Bullock, Doug. Estimating the states of the Kauffman bracket skein module. Banach Center Publications, Tome 43 (1998) pp. 23-28. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv42i1p23bwm/

[000] [1] G. Brumfiel and H. M. Hilden, SL(2) representations of finitely presented groups, Contemporary Mathematics 187 (1995). | Zbl 0838.20006

[001] [2] D. Bullock, The (2,∞)-skein module of the complement of a (2,2p+1) torus knot, J. Knot Theory Ramifications 4 no. 4 (1995) 619-632. | Zbl 0852.57003

[002] [3] D. Bullock, On the Kauffman bracket skein module of surgery on a trefoil, Pacific J. Math., to appear. | Zbl 0878.57005

[003] [4] D. Bullock, A finite set of generators for the Kauffman bracket skein algebra, preprint. | Zbl 0932.57016

[004] [5] D. Bullock, Estimating a skein module with SL2(C) characters, Proc. Amer. Math. Soc., to appear. | Zbl 0866.57005

[005] [6] M. Culler and P. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. Math. 117 (1983) 109-146. | Zbl 0529.57005

[006] [7] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Functionen, Vol. 1, B. G. Teubner, Leipzig 1897.

[007] [8] W. Goldman, The Symplectic Nature of Fundamental Groups of Surfaces, Adv. Math. 54 no. 2 (1984) 200-225. | Zbl 0574.32032

[008] [9] R. Horowitz, Characters of free groups represented in the two dimensional linear group, Comm. Pure Appl. Math. 25 (1972) 635-649. | Zbl 1184.20009

[009] [10] J. Hoste and J. H. Przytycki, The (2,∞)-skein module of lens spaces; a generalization of the Jones polynomial, J. Knot Theory Ramifications 2 no. 3 (1993) 321-333. | Zbl 0796.57005

[010] [11] J. Hoste and J. H. Przytycki, The Kauffman bracket skein module of S1×S2, Math Z. 220 (1995) 65-73. | Zbl 0826.57007

[011] [12] W. Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980), 91-103. | Zbl 0433.20033

[012] [13] H. Vogt, Sur les invariants fondamentaux des équations différentielles linéaires du second ordre, Ann. Sci. École Norm. Supér. III. Sér. 6 (1889), 3-72. | Zbl 21.0314.01