We explore the special structure of top-dimensional homology any compact triangulable space X dimension d. Since there are no (d+1)-dimensional cells, top equals cycles and is thus a free abelian group. There obvious basis, but we show that canonical embedding into group which has natural basis up to signs. This an invariant homeomorphism. circumstance gives (orientable) matroid, where in sense...

For a compact $(2n+1)$-dimensional smooth manifold, let $\mu_M : B Diff_\partial (D^{2n+1}) \to Diff (M)$ be the map that is defined by extending diffeomorphisms on an embedded disc identity. By classical result of Farrell and Hsiang, rational homotopy groups homology $ (D^{2n+1})$ are known in concordance stable range. We prove two results behaviour $\mu_M$ Firstly, it \emph{injective} gro...

Let B be a commutative algebra and A B-algebra (determined by an homomorphism ?:B?A). M. D. Staic introduced Hochschild like cohomology H•((A,B,?);A) called secondary cohomology, to describe the non-trivial deformations of A. J. Laubacher et al later obtained natural construction new chain complex C¯•(A,B,?) in process introducing cyclic (co)homology. In this paper, we establish connection betw...

In a companion paper ( arXiv:1910.03150 ) to this one, we proved that the Gromov–Witten theory of Fano orbifold line type D is governed by system Hirota Bilinear Equations. The goal prove every solution Equations determines new integrable hierarchy Lax equations. We suggest name extended D-Toda for equations, because it should be viewed as analogue Carlet’s bi-graded Toda hierarchy, which known...

We introduce homology and finite topological spaces. From the basis of that introduction, persistent homology is applied to finite spaces. We prove an equivalence between persistent homology and normal homology in the context of finite topological spaces and introduce an extended pseudometric on finite topological spaces, using the results of Minian.

We characterize the tempered part of automorphic Langlands category D-mod(Bun_G) using geometry big cell in affine Grassmannian. deduce that, for $G$ non-abelian, D-modules have no de Rham cohomology with compact supports. The latter fact boils down to a concrete statement, which we prove Ran space and some explicit t-structure estimates: non-abelian $\Sigma$ smooth curve, Borel-Moore homology ...