Yazar "Rangipour, Bahram" seçeneğine göre listele

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    Characteristic classes of foliations via SAYD-twisted cocycles
    (European Mathematical Society, 2015) Rangipour, Bahram; Sütlü, Serkan Selçuk
    We find the first non trivial “SAYD-twisted” cyclic cocycle over the groupoid action algebra under the symmetry of the affine linear transformations of the Euclidian space. We apply the cocycle to construct a characteristic map by which we transfer the characteristic classes of transversely orientable foliations into the cyclic cohomology of the groupoid action algebra. In codimension 1, our result matches with the (only explicit) computation done by Connes–Moscovici. We carry out the explicit computation in codimension 2 to present the transverse fundamental class, the Godbillon–Vey class, and the other four residual classes as cyclic cocycles on the groupoid action algebra.
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    Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebras with infinite dimensional coefficients
    (Springer Heidelberg, 2018-12-01) Rangipour, Bahram; Sütlü, Serkan Selçuk; Aliabadi, F. Yazdani
    We discuss a new strategy for the computation of the Hopf-cyclic cohomology of the Connes-Moscovici Hopf algebra Hn. More precisely, we introduce a multiplicative structure on the Hopf-cyclic complex of Hn, and we show that the van Est type characteristic homomorphism from the Hopf-cyclic complex of Hn to the Gelfand-Fuks cohomology of the Lie algebra Wn of formal vector fields on Rn respects this multiplicative structure. We then illustrate the machinery for n = 1.
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    Topological Hopf algebras and their Hopf-cyclic cohomology
    (Taylor and Francis, 2019-01-29) Rangipour, Bahram; Sütlü, Serkan Selçuk
    A natural extension of the Hopf-cyclic cohomology, with coefficients, is introduced to encompass topological Hopf algebras. The topological theory allows to work with infinite dimensional Lie algebras. Furthermore, the category of coefficients (AYD modules) over a topological Lie algebra and those over its universal enveloping (Hopf) algebra are isomorphic. For topological Hopf algebras, the category of coefficients is identified with the representation category of a topological algebra called the anti-Drinfeld double. Finally, a topological van Est type isomorphism is detailed, connecting the Hopf-cyclic cohomology to the relative Lie algebra cohomology with respect to a maximal compact subalgebra.