scholarly journals Čech cohomology and the capitulation kernel

2019 ◽  
Vol 61 (1) ◽  
pp. 95-108 ◽  
Author(s):  
Cristian D. González-Avilés
Keyword(s):  
Cech Cohomology

The Cech Cohomology of Paracompact Product Spaces

1965 ◽  
Vol 87 (1) ◽  
pp. 71 ◽  
Author(s):  
Ronald C. O'Neill
Keyword(s):  
Product Spaces ◽  
Cech Cohomology

scholarly journals Fourier transform from momentum space to twistor space

2020 ◽  
pp. 2150032
Author(s):  
Jun-ichi Note
Keyword(s):  
Fourier Transform ◽  
Momentum Space ◽  
Twistor Space ◽  
Three Dimensional ◽  
Yang Mills ◽  
The Fourier Transform ◽  
Complex Integral ◽  
Cech Cohomology ◽  
Complex Projective ◽  
Operator Representations

Several methods use the Fourier transform from momentum space to twistor space to analyze scattering amplitudes in Yang–Mills theory. However, the transform has not been defined as a concrete complex integral when the twistor space is a three-dimensional complex projective space. To the best of our knowledge, this is the first study to define it as well as its inverse in terms of a concrete complex integral. In addition, our study is the first to show that the Fourier transform is an isomorphism from the zeroth Čech cohomology group to the first one. Moreover, the well-known twistor operator representations in twistor theory literature are shown to be valid for the Fourier transform and its inverse transform. Finally, we identify functions over which the application of the operators is closed.

CROSSED PRODUCT C*-ALGEBRAS AND ALGEBRAIC TOPOLOGY

1996 ◽  
Vol 08 (04) ◽  
pp. 623-637
Author(s):  
JUDITH A. PACKER
Keyword(s):  
Algebraic Topology ◽  
Equivariant Cohomology ◽  
Automorphism Groups ◽  
Crossed Product ◽  
Fiber Bundles ◽  
Topological Invariants ◽  
C Algebras ◽  
Recent Developments ◽  
Continuous Trace ◽  
Cech Cohomology

We discuss some recent developments that illustrate the interplay between the theory of crossed products of continuous trace C*-algebras and algebraic topology, summarizing results relating topological invariants coming from the theory of fiber bundles to continuous trace C*-algebras and their automorphism groups and the structure of the associated crossed product C*-algebras. This survey article starts from the classical theory of Dixmier, Douady, and Fell, and discusses the more recent work of Echterhoff, Phillips, Raeburn, Rosenberg, and Williams, among others. The topological invariants involved are Čech cohomology, the cohomology of locally compact groups with Borel cochains of C. Moore, and the recently introduced equivariant cohomology theory of Crocker, Kumjian, Raeburn and Williams.

Moore Cohomology and Central Twisted Crossed Product C*-Algebras

1996 ◽  
Vol 48 (1) ◽  
pp. 159-174 ◽  
Author(s):  
Judith A. Packer
Keyword(s):  
Cohomology Group ◽  
Hausdorff Space ◽  
Countable Group ◽  
Equivalence Classes ◽  
Locally Compact ◽  
C Algebras ◽  
Integer Coefficients ◽  
Direct Sum ◽  
Cech Cohomology ◽  
The Relationship

AbstractLet G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟl(βX, Ζ)) ⊕ C(X, Hn(G, T)); here Ȟ1 (βX, Ζ) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C0(X) ⊗ 𝒦, and the equivariant Brauer group BrG(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.

scholarly journals ON MATRIX TYPE CORINGS, ALGEBRA COVERINGS AND ČECH COHOMOLOGY

2007 ◽  
Vol 04 (07) ◽  
pp. 1099-1105 ◽  
Author(s):  
ANDRZEJ SITARZ
Keyword(s):  
Matrix Type ◽  
Cech Cohomology

We investigate a matrix-type coring associated to a complete covering of an algebra, its Amitsur complex and propose a definition for the related Čech cohomology relative to the covering.

Blown-up Čech cohomology and Cartan’s Theorem B on real algebraic varieties

2019 ◽  
Vol 30 (09) ◽  
pp. 1950042
Author(s):  
Tomasz Kowalczyk
Keyword(s):  
Homological Dimension ◽  
Coherent Sheaves ◽  
Dimension Formula ◽  
Real Algebraic Varieties ◽  
Blowing Up ◽  
Universal Solution ◽  
Real Affine ◽  
Directed Set ◽  
Cousin Problem ◽  
Cech Cohomology

We introduce a concept of blown-up Čech cohomology for coherent sheaves of homological dimension [Formula: see text] and some quasi-coherent sheaves on a nonsingular real affine variety. Its construction involves a directed set of multi-blowups. We establish, in particular, long exact cohomology sequence and Cartan’s Theorem B. Finally, some applications are provided, including universal solution to the first Cousin problem (after blowing up).

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