$L^2$-torsion invariants and homology growth of a torus bundle over $S^1$
Kitano, Teruaki ; Morifuji, Takayuki ; Takasawa, Mitsuhiko
Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, p. 76-79 / Harvested from Project Euclid
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We introduced an infinite sequence of $L^2$-torsion invariants for surface bundles over the circle in [4]. In this note, we investigate in detail the first two terms for a torus bundle case. In particular, we show that the first invariant can be described by the asymptotic behavior of the order of the first homology group of a cyclic covering.
Publié le : 2003-04-14
Classification:  $L^2$-torsion,  hyperbolic volume,  surface bundle,  nilpotent quotient,  57Q10,  57M05,  46L10 
@article{1116443657,
     author = {Kitano, Teruaki and Morifuji, Takayuki and Takasawa, Mitsuhiko},
     title = {$L^2$-torsion invariants and homology growth of a torus bundle over $S^1$},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {79},
     number = {3},
     year = {2003},
     pages = { 76-79},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116443657}
}

Kitano, Teruaki; Morifuji, Takayuki; Takasawa, Mitsuhiko. $L^2$-torsion invariants and homology growth of a torus bundle over $S^1$. Proc. Japan Acad. Ser. A Math. Sci., Tome 79 (2003) no. 3, pp.  76-79. http://gdmltest.u-ga.fr/item/1116443657/