De Rham intersection cohomology for general perversities
| dc.creator | Saralegi-Aranguren, Martintxo E. | |
| dc.date | 2004-04-06 | |
| dc.date | 2005-07-21 | |
| dc.date.accessioned | 2026-07-07T10:19:48Z | |
| dc.date.available | 2026-07-07T10:19:48Z | |
| dc.description | For a stratified pseudomanifold $X$, we have the de Rham Theorem $ \lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} - \per{p}}{*}{X}, $ for a perversity $\per{p}$ verifying $\per{0} \leq \per{p} \leq \per{t}$, where $\per{t}$ denotes the top perversity. We extend this result to any perversity $\per{p}$. In the direction cohomology $\mapsto$ homology, we obtain the isomorphism $$ \lau{\IH}{*}{\per{p}}{X} = \lau{\IH}{\per{t} -\per{p}}{*}{X,\ib{X}{\per{p}}}, $$ where $ {\displaystyle \ib{X}{\per{p}} = \bigcup\_{S \preceq S\_{1} \atop \per{p} (S\_{1})< 0}S = \bigcup\_{\per{p} (S)< 0}\bar{S}.} $ In the direction homology $\mapsto$ cohomology, we obtain the isomorphism $$ \lau{\IH}{\per{p}}{*}{X}=\lau{\IH}{*}{\max (\per{0},\per{t} -\per{p})}{X}. $$ In our paper stratified pseudomanifolds with one-codimensional strata are allowed. | |
| dc.identifier | https://arxiv.org/abs/math/0404130 | |
| dc.identifier | http://arxiv.org/abs/math/0404130 | |
| dc.identifier | Illinois Journal of Mathematics 49 (2005) 737-758 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174646 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55N33 ; 57N80 | |
| dc.title | De Rham intersection cohomology for general perversities | |
| dc.type | text |