A Hodge theory for Alexandrov spaces with curvature bounded from above
Nat Smale · Analysis and Applications · 2014
It is shown that the Hodge theory for metric spaces based on the Alexander Spanier coboundary operator, in the presence of a measure previously developed in [4], holds for the class of compact Alexandrov spaces with curvature bounded from above. In particular, the real cohomology of the space is isomorphic to the corresponding space of harmonic co-chains.