Previous |  Up |  Next


orbit projection; proper Lie groupoid; fibration
Let $\mathcal{G} \rightrightarrows M$ be a source locally trivial proper Lie groupoid such that each orbit is of finite type. The orbit projection $M \to M/\mathcal{G}$ is a fibration if and only if $\mathcal{G}\rightrightarrows M$ is regular.
[1] Dugundji, J.: Topology. Allyn and Bacon, Inc., Boston (1966). MR 0193606 | Zbl 0144.21501
[2] Palais, R. S.: On the existence of slices for actions of non-compact Lie groups. Ann. of Math. 73 (1961), 295-323. DOI 10.2307/1970335 | MR 0126506 | Zbl 0103.01802
[3] Rainer, A.: Orbit projections as fibrations. (to appear) in Czech. Math. J., arXiv: math.DG/0610513. MR 2532388
[4] Weinstein, A.: Linearization of regular proper groupoids. J. Inst. Math. Jussieu 3 (2002), 493-511. MR 1956059 | Zbl 1043.58009
[5] Zung, N. T.: Proper groupoids and momentum maps: linearization, affinity, and convexity. Ann. Sci. Éc. Norm. Supér. 39 (2006), 841-869. MR 2292634
Partner of
EuDML logo