The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighborhood retracts of a large class of Banach spaces. On this category the authors define homology and cohomology functors with real coefficients which satisfy the Eilenberg-Steenrod axioms, but reflect the metric properties of the underlying spaces. As an example they show that the zero-dimensional homology of a space in our category is trivial if and only if the space is path connected by arcs of finite length. The homology and cohomology of a pair are, respectively, locally convex and Banach spaces that are in duality. Ignoring the topological structures, the homology and cohomology extend to all pairs of compact metric spaces. For locally acyclic spaces, the authors establish a natural isomorphism between their cohomology and the Cech cohomology with real coefficients.
Les mer
The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighbourhood retracts of a large class of Banach spaces.
Les mer
IntroductionNotation and preliminariesRectifiable chainsLipschitz chainsFlat norm and flat chainsThe lower semicontinuity of slicing massSupports of flat chainsFlat chains of finite massSupports of flat chains of finite massMeasures defined by flat chains of finite massProductsFlat chains in compact metric spacesLocalized topologyHomology and cohomology$q$-bounded pairsDimension zeroRelation to the Cech cohomologyLocally compact spacesReferences
Les mer

Produktdetaljer

ISBN
9781470423353
Publisert
2017-05-30
Utgiver
Vendor
American Mathematical Society
Vekt
200 gr
Høyde
254 mm
Bredde
178 mm
Aldersnivå
P, 06
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
115

Forfatter

Biographical note

Th. De Pauw, Universite Denis Diderot, Paris, France.

R. M. Hardt, Rice University, Houston, TX.

W. F. Pfeffer, University of California, Davis.