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Measure Homology

Student-Run Research Seminar

Speaker: Nicholas Cazet, UC Davis
Location: (Online) Zoom
Start time: Thu, May 13 2021, 11:00AM

Measure homology expands on singular homology with real coefficients. Both are functors from the category of topological spaces to the category of chain complexes of real vector spaces, and the two theories agree on spaces homotopic to CW-complexes.

Measure homology uses signed measures on function spaces to give an invariant that is useful in wild (algebraic) topology. This homology theory is isometrically isomorphic to singular homology for countable CW-complexes, thus there exists a definition of simplicial volume based on signed measures.

We will construct the measure chain complex and give recent results, including our progress on understanding the topological properties influencing the zeroth homology space.