Homological properties of stratified spaces II
Résumé
For a stratified pseudomanifold, we have the de Rham Theorem $$ \lau{\IH}{*}{\per{p}}{X} = \Hom\left(\lau{\IH}{\per{t} - \per{p}}{*}{X},\R\right), $$ for a perversity $\per{0} \leq \per{p} \leq \per{t}$, where $\per{t}$ denotes the top perversity. We extend this result to any perversity $\per{p}$. In the sense cohomology $\mapsto$ homology, we obtain the isomorphism $$ \lau{\IH}{*}{\per{p}}{X} = \Hom\left(\lau{\IH}{\per{t} -\per{p}}{*}{X,\ib{X}{\per{p}}},\R\right), $$ where $ {\displaystyle \ib{X}{\per{p}} = \bigcup_{\per{p} < 0}\overline{S} .} $ In the sense homology $\mapsto$ cohomology, we obtain the isomorphism $$ \lau{\IH}{\per{p}}{*}{X}= \Hom\left(\lau{\IH}{*}{\max ( \per{0},\per{t} -\per{p})}{X},\R\right). $$ In our context, the stratified pseudomanifolds with 1-codimensional strata are allowed.