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A Gysin sequence for semifree actions of $ {\bf S}\sp 3$

Author: Martin Saralegi
Journal: Proc. Amer. Math. Soc. 118 (1993), 1335-1345
MSC: Primary 55N33; Secondary 57S15
MathSciNet review: 1184085
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Abstract: In this work we shall consider smooth semifree (i.e., free outside the fixed point set) actions of $ {{\mathbf{S}}^3}$ on a manifold $ M$. We exhibit a Gysin sequence relating the cohomology of $ M$ with the intersection cohomology of the orbit space $ M/{{\mathbf{S}}^3}$. This generalizes the usual Gysin sequence associated with a free action of $ {{\mathbf{S}}^3}$.

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  • [1] R. Bott and L. Tu, Differential forms in algebraic topology, Graduate Texts in Math., vol. 82, Springer-Verlag, New York, 1982. MR 658304 (83i:57016)
  • [2] J. P. Brasselet, G. Hector, and M. Saralegi, Théorème de De Rham pour les variétés stratifiées, Ann. Global Anal. Geom 9 (1991), 211-243. MR 1143404 (93g:55009)
  • [3] G. Bredon, Introduction to compact transformation groups, Pure Appl. Math., vol. 46, Academic Press, New York and London, 1972. MR 0413144 (54:1265)
  • [4] J. L. Brylinsky, Equivariant intersection cohomology, preprint, I.H.E.S., June, 1986.
  • [5] W. Greub, S. Halperin, and R. Vanstone, Connections, curvature, and cohomology, Pure Appl. Math., vol. 47, Academic Press, New York and London, 1972. MR 0400275 (53:4110)
  • [6] M. Goresky and R. MacPherson, Intersection homology theory, Topology 19 (1980), 135-162. MR 572580 (82b:57010)
  • [7] -, Intersection homology. II, Invent. Math. 71 (1983), 77-129. MR 696691 (84i:57012)
  • [8] G. Hector and M. Saralegi, Intersection homology of $ {{\mathbf{S}}^1}$-actions, Trans. Amer. Math. Soc. (to appear). MR 1116314 (93j:57021)
  • [9] R. MacPherson, Intersection homology and perverse sheaves, Colloquium Lectures, Annual Meeting of the AMS, San Francisco, June 1991.
  • [10] R. Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969), 240-284. MR 0239613 (39:970)
  • [11] A. Verona, Stratified mappings--structure and triangulability, Lecture Notes in Math., vol. 1102, Springer-Verlag, New York, 1984. MR 771120 (86k:58010)

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Keywords: Gysin sequence, intersection cohomology
Article copyright: © Copyright 1993 American Mathematical Society

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