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OverviewThe 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. Full Product DetailsAuthor: Th. De Pauw , R.M. Hardt , W.F. PfefferPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.200kg ISBN: 9781470423353ISBN 10: 1470423359 Pages: 115 Publication Date: 30 May 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction Notation and preliminaries Rectifiable chains Lipschitz chains Flat norm and flat chains The lower semicontinuity of slicing mass Supports of flat chains Flat chains of finite mass Supports of flat chains of finite mass Measures defined by flat chains of finite mass Products Flat chains in compact metric spaces Localized topology Homology and cohomology $q$-bounded pairs Dimension zero Relation to the Cech cohomology Locally compact spaces ReferencesReviewsAuthor InformationTh. De Pauw, Universite Denis Diderot, Paris, France. R. M. Hardt, Rice University, Houston, TX. W. F. Pfeffer, University of California, Davis. Tab Content 6Author Website:Countries AvailableAll regions |