×

Some finiteness properties for the Reidemeister-Turaev torsion of three-manifolds. (English) Zbl 1229.57025

Summary: We prove for the Reidemeister-Turaev torsion of closed oriented three-manifolds some finiteness properties in the sense of Goussarov and Habiro, that is, with respect to some cut-and-paste operations which preserve the homology type of the manifolds. In general, those properties require the manifolds to come equipped with a Euler structure and a homological parametrization.

MSC:

57Q10 Simple homotopy type, Whitehead torsion, Reidemeister-Franz torsion, etc.
57R15 Specialized structures on manifolds (spin manifolds, framed manifolds, etc.)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1007/s00029-002-8108-0 · Zbl 1012.57015 · doi:10.1007/s00029-002-8108-0
[2] DOI: 10.1007/s00029-002-8109-z · Zbl 1012.57016 · doi:10.1007/s00029-002-8109-z
[3] DOI: 10.1007/BF02786626 · Zbl 1062.57015 · doi:10.1007/BF02786626
[4] DOI: 10.2140/gt.2006.10.1185 · Zbl 1204.58027 · doi:10.2140/gt.2006.10.1185
[5] DOI: 10.1007/s002220000045 · Zbl 0949.57010 · doi:10.1007/s002220000045
[6] DOI: 10.1016/j.top.2004.11.003 · Zbl 1071.57009 · doi:10.1016/j.top.2004.11.003
[7] DOI: 10.1142/S0218216596000278 · Zbl 0889.57015 · doi:10.1142/S0218216596000278
[8] DOI: 10.1142/S0218216502001925 · Zbl 1030.57020 · doi:10.1142/S0218216502001925
[9] DOI: 10.1007/s002080050340 · Zbl 0952.57002 · doi:10.1007/s002080050340
[10] DOI: 10.2140/gt.2001.5.75 · Zbl 1066.57015 · doi:10.2140/gt.2001.5.75
[11] Garoufalidis S., J. Differential Geom. 47 pp 257–
[12] Goussarov M., Compt. Rend. Ac. Sc. Paris Sér. I 329 pp 517–
[13] DOI: 10.2140/gt.2000.4.1 · Zbl 0941.57015 · doi:10.2140/gt.2000.4.1
[14] DOI: 10.2307/1970823 · Zbl 0255.57007 · doi:10.2307/1970823
[15] DOI: 10.2140/gt.1999.3.369 · Zbl 0929.57019 · doi:10.2140/gt.1999.3.369
[16] DOI: 10.1090/S0002-9939-1979-0529227-4 · doi:10.1090/S0002-9939-1979-0529227-4
[17] Johnson D., J. London Math. Soc. 22 pp 365–
[18] DOI: 10.1007/BF01363897 · Zbl 0409.57009 · doi:10.1007/BF01363897
[19] Laudenbach F., Astérisque 205 pp 219–
[20] DOI: 10.1016/S0040-9383(97)00035-9 · Zbl 0897.57017 · doi:10.1016/S0040-9383(97)00035-9
[21] DOI: 10.1007/s002220050256 · Zbl 0917.57008 · doi:10.1007/s002220050256
[22] DOI: 10.1007/s002080000139 · Zbl 1005.57008 · doi:10.1007/s002080000139
[23] DOI: 10.1090/S0002-9947-03-03071-X · Zbl 1028.57017 · doi:10.1090/S0002-9947-03-03071-X
[24] DOI: 10.2140/agt.2003.3.1139 · Zbl 1056.57009 · doi:10.2140/agt.2003.3.1139
[25] Matveev S. V., Math. Notices Acad. Sci. USSR 42 pp 651–
[26] DOI: 10.1215/S0012-7094-93-07017-2 · Zbl 0801.57011 · doi:10.1215/S0012-7094-93-07017-2
[27] DOI: 10.1112/S0024610799006997 · Zbl 0922.57008 · doi:10.1112/S0024610799006997
[28] DOI: 10.1515/9783110198102 · doi:10.1515/9783110198102
[29] DOI: 10.1142/S0218216596000084 · Zbl 0942.57009 · doi:10.1142/S0218216596000084
[30] Passi I. B. S., Lecture Notes in Mathematics 715, in: Group Rings and Their Augmentation Ideals (1979) · Zbl 0405.20007 · doi:10.1007/BFb0067186
[31] Perron B., Enseign. Math. 52 pp 159–
[32] DOI: 10.1090/S0002-9939-01-06128-7 · Zbl 0993.57006 · doi:10.1090/S0002-9939-01-06128-7
[33] DOI: 10.1090/S0002-9939-04-07766-4 · Zbl 1069.57010 · doi:10.1090/S0002-9939-04-07766-4
[34] Turaev V., Mat. Sb. 101 pp 252–
[35] DOI: 10.1070/IM1990v034n03ABEH000676 · Zbl 0692.57015 · doi:10.1070/IM1990v034n03ABEH000676
[36] DOI: 10.4310/MRL.1997.v4.n5.a6 · Zbl 0891.57019 · doi:10.4310/MRL.1997.v4.n5.a6
[37] DOI: 10.1007/978-3-0348-8321-4 · doi:10.1007/978-3-0348-8321-4
[38] DOI: 10.1007/978-3-0348-7999-6 · doi:10.1007/978-3-0348-7999-6
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.