Comparing homologies: Čech's theory, singular chains, integral flat chains and integral currents

DOI10.4171/RMI/489zbMath1246.49038OpenAlexW2018292892MaRDI QIDQ997812

Thierry De Pauw

Publication date: 7 August 2007

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.rmi/1180728888

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Axioms for homology theory and uniqueness theorems in algebraic topology (55N40) Other homology theories in algebraic topology (55N35) Currents in global analysis (58A25)

Related Items (5)

Linear isoperimetric inequality for normal and integral currents in compact subanalytic sets ⋮ On the equality between the infima obtained by solving various Plateau's problems ⋮ On the Almgren minimality of the product of a paired calibrated set and a calibrated manifold of codimension 1 ⋮ On the Almgren minimality of the product of a paired calibrated set with a calibrated set of codimension 1 with singularities, and new Almgren minimal cones ⋮ The coincidence of the homologies of integral currents and of integral singular chains, via cosheaves

Cites Work

• Geometry of measures in \(R^ n:\) Distribution, rectifiability, and densities
• Comparison of singular and Čech homology in locally connected spaces
• Solution of the Plateau problem for \(m\)-dimensional surfaces of varying topological type
• Cosheaves and homology
• Normal and integral currents
• Sur les théorèmes de de Rham
• Plongements lipschitziens dans ${\bbfR}\sp n$
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