De Rham’s Theorem for Orlicz Cohomology
نویسندگان
چکیده
We prove that the de Rham $ L^{\phi} -cohomology of a Riemannian manifold M admitting convenient triangulation X is isomorphic to simplicial \ell^{\phi} under some assumptions on Young function \phi . This result implies quasi-isometry invariance first cohomology.
منابع مشابه
De Rham Theorem for Extended L²-cohomology
We prove an analogue of the de Rham theorem for the extended L 2-cohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combi...
متن کاملDe Rham Theorem for Extended L 2 -cohomology
We prove an analogue of the de Rham theorem for the extended L 2-cohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combi...
متن کاملDE RHAM THEOREM FOR EXTENDED L-COHOMOLOGY M.A.SHUBIN Northeastern University
We prove an analogue of the de Rham theorem for the extended Lcohomology introduced by M.Farber [Fa]. This is done by establishing that the de Rham complex over a compact closed manifold with coefficients in a flat Hilbert bundle E of A-modules over a finite von Neumann algebra A is chain-homotopy equivalent in the sense of [GS] (i.e. with bounded morphisms and homotopy operators) to a combinat...
متن کاملA bilinear version of Orlicz-Pettis theorem
Given three Banach spaces X, Y and Z and a bounded bilinear map B : X×Y → Z, a sequence x = (xn)n ⊆ X is called B-absolutely summable if ∑∞ n=1 ‖B(xn, y)‖Z < ∞ for any y ∈ Y . Connections of this space with `weak(X) are presented. A sequence x = (xn)n ⊆ X is called B-unconditionally summable if ∑∞ n=1 |〈B(xn, y), z∗〉| < ∞ Preprint submitted to Elsevier 21 December 2007 for any y ∈ Y and z∗ ∈ Z∗...
متن کاملA Cohomology Decomposition Theorem
In [9] Jackowski and McClure gave a homotopy decomposition theorem for the classifying space of a compact Lie group G; their theorem states that for any prime p the space BG can be constructed at p as the homotopy direct limit of a specific diagram involving the classifying spaces of centralizers of elementary abelian p-subgroups of G. In this paper we will prove a parallel algebraic decomposit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Siberian Mathematical Journal
سال: 2022
ISSN: ['0037-4466', '1573-9260']
DOI: https://doi.org/10.1134/s0037446622040188