The Euler characteristic of projectively flat manifolds with amenable fundamental groups

Kim, Hyuk; Lee, Hyunkoo

doi:10.1090/S0002-9939-1993-1151814-0

The Euler characteristic of projectively flat manifolds with amenable fundamental groups
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Proc. Amer. Math. Soc. 118 (1993), 311-315 Request permission

Abstract:

The Euler characteristic of a closed projectively flat manifold with amenable fundamental group is shown to be nonnegative, and in fact zero if we further assume that the developing map is injective and the fundamental group is infinite.

References

William M. Goldman, Geometric structures on manifolds and varieties of representations, Geometry of group representations (Boulder, CO, 1987) Contemp. Math., vol. 74, Amer. Math. Soc., Providence, RI, 1988, pp. 169–198. MR 957518, DOI 10.1090/conm/074/957518
Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York-Toronto, Ont.-London, 1969. MR 0251549
Heinz Hopf, Differential geometry in the large, Lecture Notes in Mathematics, vol. 1000, Springer-Verlag, Berlin, 1983. Notes taken by Peter Lax and John Gray; With a preface by S. S. Chern. MR 707850, DOI 10.1007/978-3-662-21563-0
Morris W. Hirsch and William P. Thurston, Foliated bundles, invariant measures and flat manifolds, Ann. of Math. (2) 101 (1975), 369–390. MR 370615, DOI 10.2307/1970996
Hyuk Kim and Hyunkoo Lee, The Euler characteristic of a certain class of projectively flat manifolds, Topology Appl. 40 (1991), no. 2, 195–201. MR 1123263, DOI 10.1016/0166-8641(91)90051-M
John Milnor, On the existence of a connection with curvature zero, Comment. Math. Helv. 32 (1958), 215–223. MR 95518, DOI 10.1007/BF02564579
Tadashi Nagano and Katsumi Yagi, The affine structures on the real two-torus. I, Osaka Math. J. 11 (1974), 181–210. MR 377917

The geometry and topology of

manifolds