$L^p$ cohomology of cones and horns

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“…In [1] Brasselet, Goresky, and MacPherson conjectured that, for all p ∈ (1, ∞), the L p -cohomology is isomorphic to the corresponding intersection homology for varieties with conical singularities. Youssin [16] proved this conjecture.…”

L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

“…Indeed, Cheeger, Goresky and MacPherson in [4] stated that the L 2 -cohomology groups of the regular sets of Riemannian pseudomanifolds are isomorphic to the intersection cohomology groups with the lower middle perversities. These studies have still been developing by many mathematicians (see [5][6][7][8]). Recently, Albin, Leichtnam, Mazzeo and Piazza in [9] studied the Hodge theory on more general singular spaces, which were called Cheeger spaces.…”

Metric homology

“…Here H β 1 and H β 2 are standard β 1 -and β 2 -horns; see the notation from [1,14]. If ν(3) = 1, then MH ν loc,1 (M β 1 ,β 2 , 0) = 0 .…”