Illinois Journal of Mathematics

Coarse cohomology for families

James L. Heitsch and Steven Hurder

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We introduce coarse cohomology for families of metric spaces and develop the properties of this cohomology theory. Foliations provide the primary examples of such families and for these there are de~Rham, Čech and Alexander-Spanier versions of this theory, which are all isomorphic. We compute the coarse cohomology for a number of important examples.

Article information

Illinois J. Math., Volume 45, Number 2 (2001), 323-360.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 57R30: Foliations; geometric theory
Secondary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 55N30: Sheaf cohomology [See also 18F20, 32C35, 32L10] 57R32: Classifying spaces for foliations; Gelfand-Fuks cohomology [See also 58H10] 58H10: Cohomology of classifying spaces for pseudogroup structures (Spencer, Gelfand-Fuks, etc.) [See also 57R32]


Heitsch, James L.; Hurder, Steven. Coarse cohomology for families. Illinois J. Math. 45 (2001), no. 2, 323--360. doi:10.1215/ijm/1258138344.

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