Geodesic
Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass)
Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2175-2208 Cet article a éte moissonné depuis la source EMS Press

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This paper begins the classification of topological actions on manifolds by compact, connected, Lie groups beyond the circle group. It treats multiaxial topological actions of unitary and symplectic groups without the dimension restrictions used in earlier works by M. Davis and W. C. Hsiang on differentiable actions. The general results are applied to give detailed calculations for topological actions homotopically modeled on standard multiaxial representation spheres. In the present topological setting, Schubert calculus of complex Grassmannians surprisingly enters in the calculations, yielding a profusion of “fake” representation spheres compared with the paucity in the previously studied smooth setting.
DOI : 10.4171/jems/554
Classification : 57-XX
Keywords: Transformation group, topological manifold, stratified space, multiaxial, surgery, assembly map 
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     title = {Topological classification of multiaxial $U(n)$-actions (with an appendix by {Jared} {Bass)}},
     journal = {Journal of the European Mathematical Society},
     pages = {2175--2208},
     year = {2015},
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Sylvain Cappell; Shmuel Weinberger; Min Yan. Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass). Journal of the European Mathematical Society, Tome 17 (2015) no. 9, pp. 2175-2208. doi: 10.4171/jems/554

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