Estimating the states of the Kauffman bracket skein module

Doug Bullock

Banach Center Publications (1998)

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

Abstract

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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 characters of the fundamental group, which in turn provides estimates of the invariant.

How to cite

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Bullock, 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

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  4. [4] D. Bullock, A finite set of generators for the Kauffman bracket skein algebra, preprint. Zbl0932.57016
  5. [5] D. Bullock, Estimating a skein module with characters, Proc. Amer. Math. Soc., to appear. Zbl0866.57005
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  10. [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. [11] J. Hoste and J. H. Przytycki, The Kauffman bracket skein module of , Math Z. 220 (1995) 65-73. Zbl0826.57007
  12. [12] W. Magnus, Rings of Fricke characters and automorphism groups of free groups, Math. Z. 170 (1980), 91-103. Zbl0433.20033
  13. [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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