منابع مشابه
An Isometry Between Measure Homology and Singular Homology
In Thurston’s notes, he gives two different definitions of the Gromov norm (also called simplicial volume) of a manifold and states that they are equal but does not prove it. Gromov proves it in the special case of hyperbolic manifolds as a consequence of his proof that simplicial volume is proportional to volume. We give a proof for all differentiable manifolds. MSC: 57N65
متن کاملMeasure Homology and Singular Homology Are Isometrically Isomorphic
Measure homology is a variation of singular homology designed by Thurston in his discussion of simplicial volume. Zastrow and Hansen showed independently that singular homology (with real coefficients) and measure homology coincide algebraically on the category of CW-complexes. It is the aim of this paper to prove that this isomorphism is isometric with respect to the `1-seminorm on singular ho...
متن کاملMahler Measure , Links and Homology Growth
Let l be an oriented link of d components with nonzero Alexander polynomial ∆(u1, . . . , ud). Let Λ be a finite-index subgroup of H1(S− l) ∼= Z, and let MΛ be the corresponding abelian cover of S branched along l. The growth rate of the order of the torsion subgroup of H1(MΛ), as a suitable measure of Λ approaches infinity, is equal to the Mahler measure of ∆.
متن کاملRelative (co)homology of $F$-Gorenstein modules
We investigate the relative cohomology and relative homology theories of $F$-Gorenstein modules, consider the relations between classical and $F$-Gorenstein (co)homology theories.
متن کاملExact sequences of extended $d$-homology
In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1998
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-13851