On the Orlicz cohomology of star-bounded simplicial complexes

Abstract

We prove that the Whitney transformation induces an isomorphism between the Orlicz cohomology of a star-bounded simplicial complex and the cohomology of the corresponding Orlicz--Sullivan complex. Our main result is an extension of the isomorphism in the~$L_p$ case proved by Gol$'$dshtein, Kuz$'$minov, and Shvedov in 1988.