The Gromov norm and foliations

D. Calegari

doi:10.1007/pl00001655

Corrigendium to "The Gromov norm of the Kaehler class and the Maslov index", Asian J. Math., VOL. 7, NO. 2, 269-296, 2003

Asian Journal of Mathematics ◽

10.4310/ajm.2004.v8.n3.a1 ◽

2004 ◽

Vol 8 (3) ◽

pp. 391-394

Author(s):

Jean-Louis Clerc ◽

Bent Ørsted

Keyword(s):

Maslov Index ◽

Gromov Norm

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Erratum to: “The Gromov norm of the product of two surfaces” [Topology 44 (2005) 321–339]

Topology ◽

10.1016/j.top.2008.05.001 ◽

2008 ◽

Vol 47 (6) ◽

pp. 471-472

Author(s):

Lewis Bowen ◽

Jesús A. De Loera ◽

Mike Develin ◽

Francisco Santos

Keyword(s):

Gromov Norm

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A Natural Series for the Natural Logarithm

The Electronic Journal of Combinatorics ◽

10.37236/880 ◽

2008 ◽

Vol 15 (1) ◽

Author(s):

Oliver T. Dasbach

Keyword(s):

Power Series ◽

Infinite Series ◽

Mahler Measure ◽

Series Expansions ◽

Natural Logarithm ◽

Similar Series ◽

Power Series Expansions ◽

Gromov Norm ◽

Logarithm Function ◽

Natural Series

Rodriguez Villegas expressed the Mahler measure of a polynomial in terms of an infinite series. Lück's combinatorial $L^2$-torsion leads to similar series expressions for the Gromov norm of a knot complement. In this note we show that those formulae yield interesting power series expansions for the logarithm function. This generalizes an infinite series of Lehmer for the natural logarithm of $4$.

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Chains that realize the Gromov invariant of hyperbolic manifolds

Ergodic Theory and Dynamical Systems ◽

10.1017/s0143385797084939 ◽

1997 ◽

Vol 17 (3) ◽

pp. 643-648 ◽

Cited By ~ 9

Author(s):

DOUGLAS JUNGREIS

Keyword(s):

Hyperbolic Manifold ◽

Homology Class ◽

Hyperbolic Manifolds ◽

Uniform Measure ◽

Geodesic Boundary ◽

Maximal Volume ◽

Totally Geodesic ◽

Gromov Norm

For any closed hyperbolic manifold of dimension $n \geq 3$, suppose a sequence of $n$-cycles representing the fundamental homology class have norms converging to the Gromov invariant. We show that this sequence must converge to the uniform measure on the space of maximal-volume ideal simplices. As a corollary, we show that for a hyperbolic $n$-manifold $L$ ($n \geq 3$) with totally-geodesic boundary, the Gromov norm of ($L,\partial L$) is strictly greater than the volume of $L$ divided by the maximal volume of an ideal $n$-simplex.

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