Homogeneous and inhomogeneous manifolds
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- by Paul Gartside, David Gauld and Sina Greenwood PDF
- Proc. Amer. Math. Soc. 136 (2008), 3363-3373 Request permission
Abstract:
All metaLindelöf, and most countably paracompact, homogeneous manifolds are Hausdorff. Metacompact manifolds are never rigid. Every countable group can be realized as the group of autohomeomorphisms of a Lindelöf manifold. There is a rigid foliation of the plane.References
- Mathieu Baillif and Alexandre Gabard, Manifolds: Hausdorffness versus homogeneity, Proc. Amer. Math. Soc. 136 (2008), no. 3, 1105–1111. MR 2361887, DOI 10.1090/S0002-9939-07-09100-9
- Andreas Blass and James M. Kister, Free subgroups of the homeomorphism group of the reals, Topology Appl. 24 (1986), no. 1-3, 243–252. Special volume in honor of R. H. Bing (1914–1986). MR 872496, DOI 10.1016/0166-8641(86)90067-2
- Paul Gartside and Aneirin Glyn, Autohomeomorphism groups, Topology Appl. 129 (2003), no. 2, 103–110. MR 1961392, DOI 10.1016/S0166-8641(02)00140-2
- P. M. Gartside and R. W. Knight, Ubiquity of free subgroups, Bull. London Math. Soc. 35 (2003), no. 5, 624–634. MR 1989491, DOI 10.1112/S0024609303002194
- A. Haefliger, Sur les feuilletages des variétés de dimension $n$ par des feuilles fermées de dimension $n-1$, Colloque de Topologie de Strasbourg, 1955.
- André Haefliger and Georges Reeb, Variétés (non séparées) à une dimension et structures feuilletées du plan, Enseign. Math. (2) 3 (1957), 107–125 (French). MR 89412
- Steven G. Harris and Robert J. Low, Causal monotonicity, omniscient foliations and the shape of space, Classical Quantum Gravity 18 (2001), no. 1, 27–43. MR 1805136, DOI 10.1088/0264-9381/18/1/303
- S. W. Hawking and G. F. R. Ellis, The large scale structure of space-time, Cambridge Monographs on Mathematical Physics, No. 1, Cambridge University Press, London-New York, 1973. MR 0424186, DOI 10.1017/CBO9780511524646
- Itiro Tamura, Topology of foliations: an introduction, Translations of Mathematical Monographs, vol. 97, American Mathematical Society, Providence, RI, 1992. Translated from the 1976 Japanese edition and with an afterword by Kiki Hudson; With a foreword by Takashi Tsuboi. MR 1151624, DOI 10.1090/mmono/097
- N. M. J. Woodhouse and L. J. Mason, The Geroch group and non-Hausdorff twistor spaces, Nonlinearity 1 (1988), no. 1, 73–114. MR 928949, DOI 10.1088/0951-7715/1/1/004
Additional Information
- Paul Gartside
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- Email: gartside@math.pitt.edu
- David Gauld
- Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
- Email: d.gauld@auckland.ac.nz
- Sina Greenwood
- Affiliation: Department of Mathematics, University of Auckland, Auckland, New Zealand
- Email: s.greenwood@auckland.ac.nz
- Received by editor(s): May 22, 2007
- Received by editor(s) in revised form: August 8, 2007
- Published electronically: May 6, 2008
- Additional Notes: This work was supported in part by the Marsden Fund Council from government funding, administered by the Royal Society of New Zealand.
- Communicated by: Alexander N. Dranishnikov
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 136 (2008), 3363-3373
- MSC (2000): Primary 54D10, 54D20, 57R30, 57N05, 57S05
- DOI: https://doi.org/10.1090/S0002-9939-08-09343-X
- MathSciNet review: 2407104