Transitive actions of locally compact groups on locally contractible spaces

Journal fur die Reine und Angewandte Mathematik

Volumn 2015, Issue 702, 2015, Pages 227-243

  Hofmann, Karl H ^a   Kramer, Linus ^b  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

^b UNIVERSITY OF MÜNSTER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84928888149     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crelle-2013-0036     Document Type: Article

References (40)

1. S. M. Ageev and D. Repovsh, On the extension of actions of groups (Russian), Mat. Sb. 201 (2010), no. 2, 3-28;
2. translation in Sb. Math. 201 (2010), no. 1-2, 159-182.
3. S. A. Antonyan, Characterizing maximal compact subgroups, Arch. Math. (Basel) 98 (2012), no. 6, 555-560.
4. S. A. Antonyan and T. Dobrowolski, Locally contractible coset spaces, Forum Math., to appear.
5. V. N. Berestovski, Similarly homogeneous locally complete spaces with an intrinsic metric (Russian), Izv. Vyssh. Uchebn. Zaved. Mat. 2004 (2004), no. 11, 3-22;
6. translation in Russian Math. (Iz. VUZ) 48 (2004), no. 11, 1-19 (2005).
7. V. N. Berestovski, D. M. Halverson and D. Repovš, Locally G-homogeneous Busemann G-spaces, Differential Geom. Appl. 29 (2011), no. 3, 299-318.
8. H. Bickel, Lie-projective groups, J. Lie Theory 5 (1995), no. 1, 15-24.
9. G. E. Bredon, Introduction to compact transformation groups, Academic Press, New York 1972.
10. J. D. Dixon and B. Mortimer, Permutation groups, Grad. Texts in Math. 163, Springer-Verlag, New York 1996.
11. J. Dugundji, Topology, Allyn & Bacon, Boston 1978.
12. S. Eilenberg and N. Steenrod, Foundations of algebraic topology, Princeton Univeristy Press, Princeton 1952.
13. R. Engelking, General topology, 2nd ed., Sigma Ser. Pure Math. 6, Heldermann, Berlin 1989.
14. A. A. George Michael, On locally contractible homogeneous spaces, preprint 2012.
15. V. M. Gluškov, Structure of locally bicompact groups and Hilbert's fifth problem (Russian), Uspehi Mat. Nauk (N.S.) 12 (1957), no. 2 (74), 3-41;
16. translated in Amer. Math. Soc. Transl. (2) 15 (1960), 55-93.
17. T. Grundhöfer, N. Knarr and L. Kramer, Flag-homogeneous compact connected polygons, Geom. Dedicata 55 (1995), no. 1, 95-114.
18. T. Grundhöfer, N. Knarr and L. Kramer, Flag-homogeneous compact connected polygons. II, Geom. Dedicata 83 (2000), no. 1-3, 1-29.
19. E. Hewitt and K. A. Ross, Abstract harmonic analysis. Vol. I: Structure of topological groups, integration theory, group representations, 2nd. ed., Grundlehren Math. Wiss. 115, Springer-Verlag, Berlin 1994.
20. J. G. Hocking and G. S. Young, Topology, Addison-Wesley Publishing, Reading 1961.
21. K. H. Hofmann and M. Mislove, On the fixed point set of a compact transformation group with some applications to compact monoids, Trans. Amer. Math. Soc. 206 (1975), 137-162.
22. K. H. Hofmann and S. A. Morris, The structure of compact groups, 2nd ed., de Gruyter Stud. Math. 25,Walter de Gruyter, Berlin 2006.
23. K. H. Hofmann and S. A. Morris, Transitive actions of compact groups and topological dimension, J. Algebra 234 (2000), no. 2, 454-479.
24. K. H. Hofmann and S. A. Morris, The Lie theory of connected pro-Lie groups, EMS Tracts Math. 2, European Mathematical Society, Zürich 2007.
25. K. H. Hofmann and P. S. Mostert, Elements of compact semigroups, Charles E. Merrill Books, Columbus 1966.
26. K. H. Hofmann and K.-H. Neeb, Pro-Lie groups which are infinite-dimensional Lie groups, Math. Proc. Cambridge Philos. Soc. 146 (2009), no. 2, 351-378.
27. S. Hu, Theory of retracts, Wayne State University Press, Detroit 1965.
28. K. Iwasawa, On some types of topological groups, Ann. of Math. (2) 50 (1949), 507-558.
29. L. Kramer, Homogeneous spaces, Tits buildings, and isoparametric hypersurfaces, Mem. Amer. Math. Soc. 158 (2002), no. 752.
30. B. Madison, Semigroups on coset spaces, Duke Math. J. 36 (1969), 61-63.
31. D. Montgomery and L. Zippin, Topological transformation groups, Interscience Publishers, New York, 1955.
32. A. L. Onishchik, Topology of transitive transformation groups, Johann Ambrosius Barth, Leipzig 1994.
33. L. S. Pontrjagin, Topologische Gruppen. I, B. G. Teubner, Leipzig 1957.
34. H. Salzmann, D. Betten, T. Grundhöfer, H. Hähl, R. Löwen and M. Stroppel, Compact projective planes.With an introduction to octonion geometry, de Gruyter Exp. Math. 21, Walter de Gruyter, Berlin 1995.
35. E. G. Skljarenko, On the topological structure of locally bicompact groups and their factor spaces, Mat. Sb. (N.S.) 60 (102) (1963), 63-88;
36. translated in Amer. Math. Soc. Transl. (2) 39 (1964), 57-82.
37. M. Stroppel, Locally compact groups, EMS Textbk. Math., European Mathematical Society (EMS), Zürich 2006.
38. J. Szenthe, On the topological characterization of transitive Lie group actions, Acta Sci. Math. (Szeged) 36 (1974), 323-344.
39. F.W. Warner, Foundations of differentiable manifolds and Lie groups, corrected reprint of the 1971 edition, Grad. Texts in Math. 94, Springer-Verlag, New York 1983.
40. H. Yamabe, On the conjecture of Iwasawa and Gleason, Ann. of Math. (2) 58 (1953), 48-54.