singular cohomology
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2021 ◽  
Vol 390 ◽  
pp. 107944
Author(s):  
Christopher Schommer-Pries ◽  
Nathaniel Stapleton


2021 ◽  
pp. 2150061
Author(s):  
Xiongwei Cai

Given a crossed module of groupoids [Formula: see text], we construct (1) a natural homomorphism from the product groupoid [Formula: see text] to the crossed product groupoid [Formula: see text] and (2) a transgression map from the singular cohomology [Formula: see text] of the nerve of the groupoid [Formula: see text] to the singular cohomology [Formula: see text] of the nerve of the crossed product groupoid [Formula: see text]. The latter turns out to be identical to the transgression map obtained by Tu–Xu in their study of equivariant [Formula: see text]-theory.



2021 ◽  
Vol 23 (2) ◽  
pp. 59-68
Author(s):  
Roberto Frigerio ◽  
Andrea Maffei


2020 ◽  
Vol 275 ◽  
pp. 107014
Author(s):  
Anzor Beridze ◽  
Leonard Mdzinarishvili


2020 ◽  
pp. 1-21
Author(s):  
Abhishek Kumar Shukla ◽  
Ben Williams

Abstract We construct a scheme $B(r; {\mathbb {A}}^n)$ such that a map $X \to B(r; {\mathbb {A}}^n)$ corresponds to a degree-n étale algebra on X equipped with r generating global sections. We then show that when $n=2$ , i.e., in the quadratic étale case, the singular cohomology of $B(r; {\mathbb {A}}^n)({\mathbb {R}})$ can be used to reconstruct a famous example of S. Chase and to extend its application to showing that there is a smooth affine $r-1$ -dimensional ${\mathbb {R}}$ -variety on which there are étale algebras ${\mathcal {A}}_n$ of arbitrary degrees n that cannot be generated by fewer than r elements. This shows that in the étale algebra case, a bound established by U. First and Z. Reichstein in [6] is sharp.



Filomat ◽  
2020 ◽  
Vol 34 (2) ◽  
pp. 365-372
Author(s):  
Aneta Velkoska ◽  
Zoran Misajleski

The de Rham theorem gives a natural isomorphism between De Rham cohomology and singular cohomology on a paracompact differentiable manifold. We proved this theorem on a wider family of subsets of Euclidean space, on which we can define inner differentiability. Here we define this family of sets called tangentially locally linearly independent sets, propose inner differentiability on them, postulate usual properties of differentiable real functions and show that the integration over sets that are wider than manifolds is possible.



2019 ◽  
Vol 69 (3) ◽  
pp. 685-698 ◽  
Author(s):  
Jyoti Dasgupta ◽  
Bivas Khan ◽  
Vikraman Uma

Abstract Let X be a 2n-dimensional torus manifold with a locally standard T ≅ (S1)n action whose orbit space is a homology polytope. Smooth complete complex toric varieties and quasitoric manifolds are examples of torus manifolds. Consider a principal T-bundle p : E → B and let π : E(X) → B be the associated torus manifold bundle. We give a presentation of the singular cohomology ring of E(X) as a H*(B)-algebra and the topological K-ring of E(X) as a K*(B)-algebra with generators and relations. These generalize the results in [17] and [19] when the base B = pt. These also extend the results in [20], obtained in the case of a smooth projective toric variety, to any smooth complete toric variety.



2018 ◽  
Vol 62 (3) ◽  
pp. 625-640
Author(s):  
Thế Cu’ò’ng Nguyễn

AbstractThe algebraic EHP sequences, algebraic analogues of the EHP sequences in homotopy theory, are important tools in algebraic topology. This note will outline two new proofs of the existence of the algebraic EHP sequences. The first proof is derived from the minimal injective resolution of the reduced singular cohomology of spheres, and the second one follows Bousfield's idea using the loop functor of unstable modules.



2018 ◽  
Vol 61 (2) ◽  
pp. 272-281
Author(s):  
Matthias Franz

AbstractLet X be a CW complex with a continuous action of a topological group G. We show that if X is equivariantly formal for singular cohomology with coefficients in some field , then so are all symmetric products of X and in fact all its Γ-products. In particular, symmetric products of quasi-projective M-varieties are again M-varieties. This generalizes a result by Biswas and D’Mello about symmetric products of M-curves. We also discuss several related questions.



2018 ◽  
pp. 174-194
Author(s):  
Marvin J. Greenberg ◽  
John R. Harper
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