Topological classification of multiaxial $U\left(n\right)$-actions (with an appendix by Jared Bass)

Cappell, Sylvain, Weinberger, Shmuel, and Yan, Min. "Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass)." Journal of the European Mathematical Society 017.9 (2015): 2175-2208. <http://eudml.org/doc/277595>.

@article{Cappell2015,
abstract = {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.},
author = {Cappell, Sylvain, Weinberger, Shmuel, Yan, Min},
journal = {Journal of the European Mathematical Society},
keywords = {transformation group; topological manifold; stratified space; multiaxial; surgery; assembly map; transformation group; topological manifold; stratified space; multiaxial; surgery; assembly map},
language = {eng},
number = {9},
pages = {2175-2208},
publisher = {European Mathematical Society Publishing House},
title = {Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass)},
url = {http://eudml.org/doc/277595},
volume = {017},
year = {2015},
}

TY - JOUR
AU - Cappell, Sylvain
AU - Weinberger, Shmuel
AU - Yan, Min
TI - Topological classification of multiaxial $U(n)$-actions (with an appendix by Jared Bass)
JO - Journal of the European Mathematical Society
PY - 2015
PB - European Mathematical Society Publishing House
VL - 017
IS - 9
SP - 2175
EP - 2208
AB - 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.
LA - eng
KW - transformation group; topological manifold; stratified space; multiaxial; surgery; assembly map; transformation group; topological manifold; stratified space; multiaxial; surgery; assembly map
UR - http://eudml.org/doc/277595
ER -