No Access

A NOTE ON QUANTUM 3-MANIFOLD INVARIANTS AND HYPERBOLIC VOLUME

EFSTRATIA KALFAGIANNI

Michigan State University, E. Lansing, MI, 48823, USA

https://doi.org/10.1142/S0218216509006823Cited by:0 (Source: Crossref)

Abstract

For a closed oriented 3-manifold M and an integer r > 0, let τ_r(M) denote the SU(2) Reshetikhin–Turaev–Witten invariant of M at level r. We show that for every n > 0, and for r₁,…, r_n > 0 sufficiently large integers, there exist infinitely many non-homeomorphic hyperbolic 3-manifolds M, all of which have different hyperbolic volume, such that τ_{r_i}(M) = 1, for i = 1,…, n.

Keywords:

AMSC: 57M25, 57N10

References

C. C. Adams, J. London Math. Soc. (2) 38(3), 555 (1988). Web of Science, Google Scholar
N. Askitas and E. Kalfagianni, Topol. Appl. 126, 63 (2002), DOI: 10.1016/S0166-8641(02)00035-4. Crossref, Web of Science, Google Scholar
D. Futer, E. Kalfagianni and J. S. Purcell, J. Differential Geom. 78(3), 429 (2008). Crossref, Web of Science, Google Scholar
S. Garoufalidis, J. Knot Theory Ramifications 4, 441 (1996). Google Scholar
R. M. Kashaev, Lett. Math. Phys. 39(3), 269 (1997), DOI: 10.1023/A:1007364912784. Crossref, Web of Science, Google Scholar
E. Kalfagianni, Algebr. Geom. Topol. 4, 1111 (2004), DOI: 10.2140/agt.2004.4.1111. Crossref, Google Scholar
A. Kawauchi, J. Knot Theory Ramifications 3(1), 25 (1994), DOI: 10.1142/S0218216594000058. Link, Google Scholar
R. Kirby and P. Melvin, Invent. Math. 105(3), 473 (1991), DOI: 10.1007/BF01232277. Crossref, Web of Science, Google Scholar
M. Lackenby, Comment. Math. Helv. 71, 664 (1996), DOI: 10.1007/BF02566441. Crossref, Web of Science, Google Scholar
H. Murakami and J. Murakami, Acta Math. 186(1), 85 (2001), DOI: 10.1007/BF02392716. Crossref, Web of Science, Google Scholar
H. Murakami, Recent Progress Towards the Volume Conjecture 1172, 70 (2000). Google Scholar
N. Reshetikhin and V. Turaev, Invent. Math. 103(3), 547 (1991), DOI: 10.1007/BF01239527. Crossref, Web of Science, Google Scholar
W. Thurston, The Geometry and Topology of 3-Manifolds, http://www.msri.org/publications/books/gt3m . Google Scholar