Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Global invariants for measured foliations


Author: Steven Hurder
Journal: Trans. Amer. Math. Soc. 280 (1983), 367-391
MSC: Primary 57R30; Secondary 28D20, 57R20
DOI: https://doi.org/10.1090/S0002-9947-1983-0712266-3
MathSciNet review: 712266
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: New exotic invariants for measured foliations are constructed, which we call the $ \mu $-classes of a pair $ (\mathcal{F},\mu)$. The dependence of the $ \mu $-classes on the geometry of the foliation $ \mathcal{F}$ is examined, and the dynamics of a foliation is shown to determine the $ \mu $-classes in many cases. We use the $ \mu $-classes to study the classifying space $ B{\Gamma_{S{L_q}}}$ of foliations with a transverse invariant volume form, and we show the homotopy groups of $ B{\Gamma _{S{L_q}}}$ are uncountably generated starting in degrees $ q + 3$. New invariants for groups of volume preserving diffeomorphisms also arise from the $ \mu $-classes; these invariants are nontrivial and related to the geometric aspects of the group action. Relations between the $ \mu $-classes and the secondary classes of a foliation are exhibited.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57R30, 28D20, 57R20

Retrieve articles in all journals with MSC: 57R30, 28D20, 57R20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1983-0712266-3
Keywords: Foliations, invariant measures, characteristic classes, group homology, geometry of foliations
Article copyright: © Copyright 1983 American Mathematical Society

American Mathematical Society