Characteristic classes of foliations

Bernshtein, I. N.; Rosenfeld, Bryn

doi:10.1007/bf01075512

Cited by 13 publications

(21 citation statements)

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“…It also turns out that our function Θī(ξ) is the flat connection arising from the foliation problem as prescribed by Fuks in [15,17], the algorithm is clearly laid out in the latter reference. The same procedure is come upon independently by a number of authors [18,14], in [14] it is also explained the need to restrict the cocycle to be basic, that is, the cocyle is invariant under sp(2n) transformations, and if any of the functions f i in (4.4) is quadratic, the cochain vanishes. Both properties are clearly satisfied by our path integral construction and are crucial for the later analysis of invariance properties of our characteristic classes.…”

Section: Characteristic Classes From the Rw Bf-rw And Cs-rw Modelsmentioning

confidence: 99%

Equivariant Rozansky–Witten classes and TFTs

Kallen

Qiu²,

Zabzine

2013

Journal of Geometry and Physics

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We first construct the Rozansky-Witten model coupled to BF theory and Chern-Simons theory using the Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) method. Then we apply the machinery developed in some earlier papers about AKSZ theories and characteristic classes to these concrete models: the BF-Rozansky-Witten model and the Chern-Simons-Rozansky-Witten model. In the former case, we obtain characteristic classes on the target hyperKähler manifold equipped with a group action as a generalization of the original Rozansky-Witten classes. We also give the prescription for similar classes associated with a holomorphic symplectic manifold and demonstrate the invariance of such classes explicitly.

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Section: Characteristic Classes From the Rw Bf-rw And Cs-rw Modelsmentioning

confidence: 99%

Equivariant Rozansky–Witten classes and TFTs

Kallen

Qiu²,

Zabzine

2013

Journal of Geometry and Physics

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“…There are a variety of expositions on this topic; we select a few aspects of the theory to discuss, based on the author's preferences. The reader can confer with any of the following general references for more details: [21,22,30,32,33,35,36,48,94,95,100,102,184,186,187,206,236,258]. The reader is cautioned that notation in these papers is not particularly consistent between various authors.…”

Section: Secondary Characteristic Classesmentioning

confidence: 99%

Classifying foliations

Hurder¹

2009

Foliations, Geometry, and Topology

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Abstract. We give a survey of the approaches to classifying foliations, starting with the Haefliger classifying spaces and the various results and examples about the secondary classes of foliations. Various dynamical properties of foliations are introduced and discussed, including expansion rate, local entropy, and orbit growth rates. This leads to a decomposition of the foliated space into Borel or measurable components with these various dynamical types. The dynamical structure is compared with the classification via secondary classes.1991 Mathematics Subject Classification. Primary 22F05, 37C85, 57R20, 57R32, 58H05, 58H10; Secondary 37A35, 37A55, 37C35 .

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“…Next, if we write ∆α = k α (0) ⊗ α (1) we have: π(α)(ω 0 ω 1 )(g) = h * (α)(g)ω 0 ω 1 (g) = h * (α)(g)…”

Section: Id : M → M Is In γmentioning

confidence: 99%

Secondary characteristic classes and cyclic cohomology of Hopf algebras

Gorokhovsky

2002

Topology

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Let X be a manifold on which discrete (pseudo)group of diffeomorphisms Γ acts, and let E be a Γ-equivariant vector bundle on X. We give a construction of cyclic cocycles on the cross product algebra C ∞ 0 (X) ⋊ Γ representing the equivariant characteristic classes of E. Our formulas generalize Connes' Godbillon-Vey cyclic cocycle. An essential tool of our construction is Connes-Moscovici's theory of cyclic cohomology of Hopf algebras.

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Characteristic classes of foliations

Cited by 13 publications

References 0 publications

Equivariant Rozansky–Witten classes and TFTs

Equivariant Rozansky–Witten classes and TFTs

Classifying foliations

Secondary characteristic classes and cyclic cohomology of Hopf algebras

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