Characteristic classes of transversely homogeneous foliations

Authors:
Chal Benson and David B. Ellis

Journal:
Trans. Amer. Math. Soc. **289** (1985), 849-859

MSC:
Primary 57R32; Secondary 53C12

DOI:
https://doi.org/10.1090/S0002-9947-1985-0784016-8

MathSciNet review:
784016

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Abstract | References | Similar Articles | Additional Information

Abstract: The foliations studied in this paper have transverse geometry modeled on a homogeneous space with transition functions given by the left action of . It is shown that the characteristic classes for such a foliation are determined by invariants of a certain flat bundle. This is used to prove that when is semisimple, the characteristic classes are rigid under smooth deformations, extending work of Brooks, Goldman and Heitsch.

**[1]**D. Baker,*On a class of foliations and the evaluation of their characteristic classes*, Comment. Math. Helv.**53**(1978), 334-363. MR**0494144 (58:13073)****[2]**R. Blumenthal,*Transversely homogeneous foliations*, Ann. Inst. Fourier (Grenoble)**29**(1979), 143-158. MR**558593 (81h:57011)****[3]**R. Brooks and W. Goldman,*The Godbillon-Vey invariant of a transversely homogeneous foliation*, Trans. Amer. Math. Soc.**286**(1984), 651-664. MR**760978 (86a:53035)****[4]**C. Chevalley and S. Eilenberg,*Cohomology theory of Lie groups and Lie algebras*, Trans. Amer. Math. Soc.**63**(1948), 85-124. MR**0024908 (9:567a)****[5]**D. B. Fuks,*Cohomology of infinite dimensional Lie algebras and characteristic classes for foliations*, J. Soviet Math.**11**(1979), 922-980. MR**513337 (80g:57039)****[6]**J. Heitsch,*Deformations of secondary characteristic classes*, Topology**12**(1973), 381-388. MR**0321106 (47:9639)****[7]**-,*Independent variation of secondary classes*, Ann. of Math. (2)**108**(1978), 421-460. MR**512428 (80b:57022)****[8]**-,*Secondary invariants of transversely homogeneous foliations*, preprint.**[9]**S. Hurder,*On the secondary classes of foliations with trivial normal bundles*, Comment. Math. Helv.**56**(1981), 307-326. MR**630956 (83g:57017)****[10]**F. W. Kamber and Ph. Tondeur,*Foliated bundles and characteristic classes*, Lecture Notes in Math., vol. 493, Springer-Verlag, Berlin and New York, 1975. MR**0402773 (53:6587)****[11]**-, -*foliations and their characteristic classes*, Bull. Amer. Math. Soc.**84**(1978), 1086-1124. MR**508449 (80b:57024)****[12]**S. Kolayashi and K. Nomizu,*Foundations of differential geometry*, Vol. 2, Wiley, New York, 1969.**[13]**S. Nishikawa and H. Sato,*On characteristic classes of Riemannian, conformal and projective foliations*, J. Math. Soc. Japan**28**(1976), 224-241. MR**0400255 (53:4090)****[14]**H. Pittie,*Characteristic classes of foliations*, Pitman, London, 1976. MR**0454988 (56:13229)****[15]**-,*The secondary characteristic classes of parabolic foliations*, Comment. Math. Helv.**54**(1979), 601-614. MR**552679 (82h:57022)****[16]**W. P. Thurston,*Non cobordant foliations of*, Bull. Amer. Math. Soc.**78**(1972), 511-514. MR**0298692 (45:7741)**

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0784016-8

Article copyright:
© Copyright 1985
American Mathematical Society