Illinois Journal of Mathematics

Coarse cohomology for families

James L. Heitsch and Steven Hurder

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138344

Digital Object Identifier
doi:10.1215/ijm/1258138344

Mathematical Reviews number (MathSciNet)
MR1878608

Zentralblatt MATH identifier
1009.57036

Subjects
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]

Citation

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


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