# Estimating the states of the Kauffman bracket skein module

Banach Center Publications (1998)

- Volume: 42, Issue: 1, page 23-28
- ISSN: 0137-6934

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topBullock, Doug. "Estimating the states of the Kauffman bracket skein module." Banach Center Publications 42.1 (1998): 23-28. <http://eudml.org/doc/208809>.

@article{Bullock1998,

abstract = {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 $SL_2(C)$ characters of the fundamental group, which in turn provides estimates of the invariant.},

author = {Bullock, Doug},

journal = {Banach Center Publications},

language = {eng},

number = {1},

pages = {23-28},

title = {Estimating the states of the Kauffman bracket skein module},

url = {http://eudml.org/doc/208809},

volume = {42},

year = {1998},

}

TY - JOUR

AU - Bullock, Doug

TI - Estimating the states of the Kauffman bracket skein module

JO - Banach Center Publications

PY - 1998

VL - 42

IS - 1

SP - 23

EP - 28

AB - 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 $SL_2(C)$ characters of the fundamental group, which in turn provides estimates of the invariant.

LA - eng

UR - http://eudml.org/doc/208809

ER -

## References

top- [1] G. Brumfiel and H. M. Hilden, SL(2) representations of finitely presented groups, Contemporary Mathematics 187 (1995). Zbl0838.20006
- [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. Zbl0852.57003
- [3] D. Bullock, On the Kauffman bracket skein module of surgery on a trefoil, Pacific J. Math., to appear. Zbl0878.57005
- [4] D. Bullock, A finite set of generators for the Kauffman bracket skein algebra, preprint. Zbl0932.57016
- [5] D. Bullock, Estimating a skein module with $S{L}_{2}\left(C\right)$ characters, Proc. Amer. Math. Soc., to appear. Zbl0866.57005
- [6] M. Culler and P. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. Math. 117 (1983) 109-146. Zbl0529.57005
- [7] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Functionen, Vol. 1, B. G. Teubner, Leipzig 1897.
- [8] W. Goldman, The Symplectic Nature of Fundamental Groups of Surfaces, Adv. Math. 54 no. 2 (1984) 200-225. Zbl0574.32032
- [9] R. Horowitz, Characters of free groups represented in the two dimensional linear group, Comm. Pure Appl. Math. 25 (1972) 635-649. Zbl1184.20009
- [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. Zbl0796.57005
- [11] J. Hoste and J. H. Przytycki, The Kauffman bracket skein module of ${S}^{1}\times {S}^{2}$, Math Z. 220 (1995) 65-73. Zbl0826.57007
- [12] W. Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980), 91-103. Zbl0433.20033
- [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. Zbl21.0314.01

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