Homology of Normal Chains and Cohomology of Charges

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...

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Hauptverfasser: De Pauw, Th, Hardt, R. M., Pfeffer, W. F.
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 2017
Ausgabe:1
Schriftenreihe:Memoirs of the American Mathematical Society
Schlagworte:
Algebraic topology
Banach spaces
Cohomology operations
Mathematical analysis
Flat chains
normal chains
charges
homology
cohomology
ISBN:9781470423353, 1470423359
ISSN:0065-9266, 1947-6221
Online-Zugang:Volltext
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Inhaltsangabe:
  • Introduction -- 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 -- <inline-formula content-type="math/mathml"> q q </inline-formula>-bounded pairs -- Dimension zero -- Relation to the Čech cohomology -- Locally compact spaces
  • Cover -- Title page -- 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. -bounded pairs -- Chapter 15. Dimension zero -- Chapter 16. Relation to the Čech cohomology -- Chapter 17. Locally compact spaces -- References -- Back Cover