The Gysin Sequence for S-actions on Stratified Pseudomanifolds

For any stratified pseudomanifold X and any action of the unit circle S on X preserving the stratification and the local structure; the orbit space X/S is also a stratified pseudomanifold. For each perversity q in X the orbit map π : X → X/S induces a Gysin sequence relating the q-intersection cohomologies of X and X/S. The third term of this sequence can be given by means of a spectral sequence on X/S whose second term is the cohomology of the fixed points’ set X 1 with values on a constructible sheaf. The above statements generalize a previous work on stratified pseudomanifolds with length 1.