Intersection cohomology of [formula omitted]1-actions on pseudomanifolds

Abstract

For any smooth free action of the unit circle S 1 in a manifold M; the Gysin sequence of M is a long exact sequence relating the DeRham cohomologies of M and its orbit space M S 1. If the action is not free then M S 1 is not a manifold but a stratified pseudomanifold and there is a Gysin sequence relating the DeRham cohomology of M with the intersection cohomology of M S 1. In this work we extend the above statements for any stratified pseudomanifold X of length 1, whenever the action of S 1 preserves the local structure. We give a Gysin sequence relating the intersection cohomologies of X and X S 1 with a third terni G , the Gysin terni; whose cohomology depends on basic cohomological data of two flavors: global data concerns the Euler class induced by the action, local data relates the Gysin terni and the cohomology of the fixed strata with values on a locally trivial presheaf.