$L^2$-torsion invariants and homology growth of a torus bundle over $S^1$

Autor:	Takayuki Morifuji, Teruaki Kitano, Mitsuhiko Takasawa
Rok vydání:	2003
Předmět:	Pure mathematics Torus bundle 46L10 General Mathematics surface bundle Torus Homology (mathematics) Algebra 57M05 Mathematics::K-Theory and Homology 57Q10 Torsion (algebra) $L^2$-torsion Invariant (mathematics) Mathematics::Symplectic Geometry hyperbolic volume nilpotent quotient Mathematics
Zdroj:	Proc. Japan Acad. Ser. A Math. Sci. 79, no. 4 (2003), 76-79
ISSN:	0386-2194
DOI:	10.3792/pjaa.79.76
Popis:	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.
Databáze:	OpenAIRE
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