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A NOTE ON MEASURE HOMOLOGY

Published online by Cambridge University Press:  13 August 2013

ROBERTO FRIGERIO
ROBERTO FRIGERIO*
Affiliation:
Dipartimento di Matematica Università di Pisa Largo B. Pontecorvo 5, Pisa 56127, Italy e-mail: frigerio@dm.unipi.it
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Abstract

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Measure homology was introduced by Thurston (W. P. Thurston, The geometry and topology of 3-manifolds, mimeographed notes (Princeton University Press, Princeton, NJ, 1979)) in order to compute the simplicial volume of hyperbolic manifolds. Berlanga (R. Berlanga, A topologised measure homology, Glasg. Math. J. 50 (2008), 359–369) endowed measure homology with the structure of a graded, locally convex (possibly non-Hausdorff) topological vector space. In this paper we completely characterize Berlanga's topology on measure homology of CW-complexes, showing in particular that it is Hausdorff. This answers a question posed by Berlanga.

Keywords

55N35
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 56 , Issue 1 , January 2014 , pp. 87 - 92
Copyright
Copyright © Glasgow Mathematical Journal Trust 2013 

References

REFERENCES

1.Berlanga, R., A topologised measure homology, Glasg. Math. J. 50 (2008), 359–369.Google Scholar
2.Eilenberg, S. and Steenrod, N. E., Foundations of algebraic topology (Princeton University Press, Princeton, NJ, 1952).CrossRefGoogle Scholar
3.Frigerio, R., (Bounded) continuous cohomology and Gromov's proportionality principle, Manuscripta Math. 134 (2011), 435–474.Google Scholar
4.Gromov, M., Volume and bounded cohomology, Inst. Hautes Études Sci. Publ. Math. 56 (1982), 5–99.Google Scholar
5.Hansen, S. K., Measure homology, Math. Scand. 83 (1998), 205–219.CrossRefGoogle Scholar
6.Kelley, J. L. and Namioka, I., Linear topological spaces, Graduate Texts in Mathematics, No. 36 (Springer-Verlag, New York, NY, 1976).Google Scholar
7.Löh, C., Measure homology and singular homology are isometrically isomorphic, Math. Z. 253 (2006), 197–218.Google Scholar
8.Löh, C., Isomorphisms in l 1-homology, Münster J. Math. 1 (2008), 237–266.Google Scholar
9.Milnor, J., On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280.Google Scholar
10.Thurston, W. P., The geometry and topology of 3-manifolds, mimeographed notes (Princeton University Press, Princeton, NJ, 1979).Google Scholar
11.Zastrow, A., On the (non)-coincidence of Milnor-Thurston homology theory with singular homology theory, Pacific J. Math. (1998), 186 (2), 369–396.Google Scholar