| Description |
1 online resource (v, 115 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 247, number 1172 |
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Memoirs of the American Mathematical Society ; no. 1172.
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| Contents |
Introduction Chapter 1. Notation and preliminaries Chapter 2. Rectifiable chains Chapter 3. Lipschitz chains Chapter 4. Flat norm and flat chains Chapter 5. The lower semicontinuity of slicing mass Chapter 6. Supports of flat chains Chapter 7. Flat chains of finite mass Chapter 8. Supports of flat chains of finite mass Chapter 9. Measures defined by flat chains of finite mass Chapter 10. Products Chapter 11. Flat chains in compact metric spaces Chapter 12. Localized topology Chapter 13. Homology and cohomology Chapter 14. q-bounded pairs Chapter 15. Dimension zero Chapter 16. Relation to the Čech cohomology Chapter 17. Locally compact spaces |
| Summary |
We 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 we 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 we 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, we establish a natural isomorphism between our cohomology and the Čech cohomology with real coefficients |
| Notes |
"Volume 247, number 1172 (fifth of 7 numbers), May 2017." |
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Flat chains, normal chains, charges, homology, cohomology |
| Bibliography |
Includes bibliographical references (pages 113-115) |
| Notes |
Print version record |
| Subject |
Algebraic topology.
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Cohomology operations.
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Mathematical analysis.
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Banach spaces.
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Algebraic topology
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Banach spaces
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Cohomology operations
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Mathematical analysis
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| Form |
Electronic book
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| Author |
Hardt, R. (Robert), 1945- author.
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Pfeffer, Washek F., author
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American Mathematical Society, publisher.
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| ISBN |
9781470437053 |
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1470437058 |
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