WebCombinatorial Hodge Theory and a Geometric Approach to Ranking Combinatorial Hodge Theory Discrete Differential Geometry. Curl. Definition For each triangle … WebJul 18, 2001 · This Hodge decomposition is encoded in an action of the discrete group $\mathbb{C}^{\times \delta}$ on the object $(X\otimes \mathbb{C})^{sch}$ and is shown to recover the usual Hodge decomposition on cohomology, the Hodge filtration on the pro-algebraic fundamental group as defined by C.Simpson, and in the simply connected …

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WebWe provide and prove a discrete version of the Hodge decomposition theorem. The goal of this work is to develop a satisfactory discrete model of the de Rham–Hodge theory … WebHodge theory on a simplicial complex In order to motivate the general Hodge theorem, we work this out for a finite simplicial complex. Let K = (V,Σ) be a finite simplicial complex. ... to ∂, and let ∆ = ∂∂∗ +∂∗∂. ∆ is the discrete Laplacian. Lemma 7.1.1. Let α be a cochain. The following are equivalent: iron together

Discrete de Rham-Hodge cohomology theory: application to …

WebFeb 19, 2015 · Chern-Weil theory, ∞-Chern-Weil theory. connection on a bundle, connection on an ∞-bundle. differential cohomology. ordinary differential cohomology, Deligne complex. differential K-theory. differential cobordism cohomology. parallel transport, higher parallel transport, fiber integration in differential cohomology. holonomy, higher … WebSome Problems in “classical” algebraicK-theory. In: AlgebraicK-Theory, II. Lecture Notes in Mathematics, No.342. Berlin Heidelberg New York: Springer 1972. Google Scholar ... WebTheorem 1.3.1 (Main theorem of Hodge theory). Consider the Laplace oper-ator : A k(X) !A (X). 4 (1) There is an orthogonal direct sum decomposition Ak(X) = Hk(X) Im : (2) dim R Hk(X) <1. We will not prove this theorem since its proof uses advanced tools of functional analysis. The key ingredient of the proof is the fact that is a self-adjoint iron tomato bakery