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HEEGAARD GENUS, CUT NUMBER, WEAK p-CONGRUENCE, AND QUANTUM INVARIANTS

PATRICK M. GILMER

Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA

https://doi.org/10.1142/S021821650900749XCited by:2 (Source: Crossref)

Abstract

We use quantum invariants to define a 3-manifold invariant j_p which lies in the non-negative integers. We relate j_p to the Heegaard genus, and the cut number. We show that j_p is an invariant of weak p-congruence.

Keywords:

AMSC: 57M27

References

N. A'Campo, TQFT, computations and experiments, preprint , arXiv:math.GT/0312016 . Google Scholar
S. Akbulut and H. King, Pacific J. Math. 150(2), 201 (1991). Crossref, Web of Science, Google Scholar
C. Blanchetet al., Topology 31, 685 (1992), DOI: 10.1016/0040-9383(92)90002-Y. Crossref, Web of Science, Google Scholar
C. Blanchetet al., Topology 34, 883 (1995), DOI: 10.1016/0040-9383(94)00051-4. Crossref, Web of Science, Google Scholar
T. Cochran and P. Melvin, Topology 40, 96 (2001), DOI: 10.1016/S0040-9383(99)00056-7. Google Scholar
M. Dabkowski and J. Przytycki, Proc. Natl. Acad. Sci. USA 101, 17357 (2004), DOI: 10.1073/pnas.0406098101. Crossref, Web of Science, Google Scholar
P. M. Gilmer, Duke Math. J. 125, 389 (2004), DOI: 10.1215/S0012-7094-04-12527-8. Crossref, Web of Science, Google Scholar
P. M. Gilmer, Algebr. Geom. Topol. 7, 1767 (2007), DOI: 10.2140/agt.2007.7.1767. Crossref, Web of Science, Google Scholar
P. M. Gilmer, J. Knot Theory Ramifications 16, 1357 (2007), DOI: 10.1142/S021821650700583X. Link, Web of Science, Google Scholar
P. M. Gilmer and G. Masbaum, Ann. Sci. Ecole Norm. Super. 40, 815 (2007). Crossref, Web of Science, Google Scholar
P. M. Gilmer and G. Masbaum, Integral TQFT for a one-holed torus, preprint , arXiv:0908.2796 . Google Scholar
P. M. Gilmer, G. Masbaum and P. van Wamelen, Comment. Math. Helv. 79, 260 (2004), DOI: 10.1007/s00014-004-0801-5. Crossref, Web of Science, Google Scholar
P. M. Gilmer and K. Qazaqzeh, Acta Mat. Vietnamica 33, 279 (2008). Google Scholar
W. Jaco, J. Austral. Math. Soc. 14, 411 (1972), DOI: 10.1017/S1446788700011034. Crossref, Google Scholar
A. Hatcher, Topol. Appl. 40, 189 (1991), DOI: 10.1016/0166-8641(91)90050-V. Crossref, Web of Science, Google Scholar
L. H. Kauffman and S. Lins , Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds , Annals of Mathematics Studies 134 ( Princeton University Press , 1994 ) . Crossref, Google Scholar
M. Lackenby, Comment. Math. Helv. 71, 664 (1996), DOI: 10.1007/BF02566441. Crossref, Web of Science, Google Scholar
W. B. R. Lickorish, J. Knot Theory Ramifications 2, 171 (1993), DOI: 10.1142/S0218216593000118. Link, Google Scholar
G. Masbaum and P. Vogel, Pacific J. Math. 164, 361 (1994). Crossref, Web of Science, Google Scholar
G. Masbaum and J. Roberts, Math. Proc. Cambridge Philos. Soc. 121, 443 (1997), DOI: 10.1017/S0305004196001624. Crossref, Web of Science, Google Scholar
H. Murakami, Math. Proc. Cambridge Philos. Soc. 117, 237 (1995), DOI: 10.1017/S0305004100073084. Crossref, Web of Science, Google Scholar
Y. Nakanishi, Osaka J. Math. 27, 207 (1990). Web of Science, Google Scholar
PARI/GP, version 2.1.6, Bordeaux (2005), http://pari.math.u-bordeaux.fr/ . Google Scholar