Orbit projections as fibrations

Armin Rainer

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 2, page 529-538
  • ISSN: 0011-4642

Abstract

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The orbit projection π M → M / G of a proper G -manifold M is a fibration if and only if all points in M are regular. Under additional assumptions we show that π is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: π is a G -quasifibration if and only if all points are regular.

How to cite

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Rainer, Armin. "Orbit projections as fibrations." Czechoslovak Mathematical Journal 59.2 (2009): 529-538. <http://eudml.org/doc/37938>.

@article{Rainer2009,
abstract = {The orbit projection $\pi \: M \rightarrow M/G$ of a proper $G$-manifold $M$ is a fibration if and only if all points in $M$ are regular. Under additional assumptions we show that $\pi $ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $\pi $ is a $G$-quasifibration if and only if all points are regular.},
author = {Rainer, Armin},
journal = {Czechoslovak Mathematical Journal},
keywords = {orbit projection; proper $G$-manifold; fibration; quasifibration; orbit projection; proper -manifold; fibration; quasifibration},
language = {eng},
number = {2},
pages = {529-538},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Orbit projections as fibrations},
url = {http://eudml.org/doc/37938},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Rainer, Armin
TI - Orbit projections as fibrations
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 2
SP - 529
EP - 538
AB - The orbit projection $\pi \: M \rightarrow M/G$ of a proper $G$-manifold $M$ is a fibration if and only if all points in $M$ are regular. Under additional assumptions we show that $\pi $ is a quasifibration if and only if all points are regular. We get a full answer in the equivariant category: $\pi $ is a $G$-quasifibration if and only if all points are regular.
LA - eng
KW - orbit projection; proper $G$-manifold; fibration; quasifibration; orbit projection; proper -manifold; fibration; quasifibration
UR - http://eudml.org/doc/37938
ER -

References

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  1. Consequently, using the fact that G G/H, G G/K are fibrations, we obtain the commuting diagram n+1 (G) n+1 (G) // n+1 (G/H) // n+1 (G/K) // n (H) // n (K) // n (G) // n (G), n (G/H) , n (G/K) 

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