scholarly journals Nontrivial Deformation of a Trivial Bundle

2014 ◽  
Author(s):  
Piotr M. Hajac
Keyword(s):  
Trivial Bundle ◽  
Nontrivial Deformation

scholarly journals Riemannian foliations with Ehresmann connection

2018 ◽  
Vol 20 (4) ◽  
pp. 395-407
Author(s):  
N. I. Zhukova
Keyword(s):  
Linear Connection ◽  
Riemannian Foliation ◽  
Minimal Set ◽  
Foliated Manifold ◽  
Trivial Bundle ◽  
Riemannian Foliations ◽  
Ehresmann Connection ◽  
The Family ◽  
Leaf Space ◽  
Complete Riemannian Manifolds

It is shown that the structural theory of Molino for Riemannian foliations on compact manifolds and complete Riemannian manifolds may be generalized to a Riemannian foliations with Ehresmann connection. Within this generalization there are no restrictions on the codimension of the foliation and on the dimension of the foliated manifold. For a Riemannian foliation (M,F) with Ehresmann connection it is proved that the closure of any leaf forms a minimal set, the family of all such closures forms a singular Riemannian foliation (M,F¯¯¯¯). It is shown that in M there exists a connected open dense F¯¯¯¯-saturated subset M0 such that the induced foliation (M0,F¯¯¯¯|M0) is formed by fibers of a locally trivial bundle over some smooth Hausdorff manifold. The equivalence of some properties of Riemannian foliations (M,F) with Ehresmann connection is proved. In particular, it is shown that the structural Lie algebra of (M,F) is equal to zero if and only if the leaf space of (M,F) is naturally endowed with a smooth orbifold structure. Constructed examples show that for foliations with transversally linear connection and for conformal foliations the similar statements are not true in general.

scholarly journals On images and inverse images of Weierstrass points

1978 ◽  
Vol 19 (2) ◽  
pp. 125-128
Author(s):  
R. F. Lax
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Compact Riemann Surface ◽  
Holomorphic Vector Bundle ◽  
Compact Complex Manifold ◽  
Trivial Bundle ◽  
Weierstrass Points ◽  
Complex Dimension ◽  
Holomorphic Sections ◽  
Image Position

The classical theory of Weierstrass points on a compact Riemann surface is well-known (see, for example, [3]). Ogawa [6] has defined generalized Weierstrass points. Let Y denote a compact complex manifold of (complex) dimension n. Let E denote a holomorphic vector bundle on Y of rank q. Let Jk(E) (k = 0, 1, …) denote the holomorphic vector bundle of k-jets of E [2, p. 112]. Put rk(E) = rank Jk(E) = q.(n + k)!/n!k!. Suppose that Γ(E), the vector space of global holomorphic sections of E, is of dimension γ(E)>0. Consider the trivial bundle Y × Γ(E) and the mapwhich at a point Q∈Y takes a section of E to its k-jet at Q. Put μ = min(γ(E),rk(E)).

scholarly journals Some remarks on representations up to homotopy

2016 ◽  
Vol 13 (03) ◽  
pp. 1650024
Author(s):  
Giorgio Trentinaglia ◽  
Chenchang Zhu
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Compact Group ◽  
Compact Groups ◽  
Quantum Field ◽  
Algebraic Quantum Field Theory ◽  
Trivial Bundle ◽  
Finite Dimensional ◽  
Algebraic Quantum

Motivated by the study of the interrelation between functorial and algebraic quantum field theory (AQFT), we point out that on any locally trivial bundle of compact groups, representations up to homotopy are enough to separate points by means of the associated representations in cohomology. Furthermore, we observe that the derived representation category of any compact group is equivalent to the category of ordinary (finite-dimensional) representations of the group.

scholarly journals First and second cohomology group of a bu ndle

2012 ◽  
Vol 20 (2) ◽  
pp. 71-78
Author(s):  
Adelina Manea
Keyword(s):  
Vector Bundle ◽  
Cohomology Group ◽  
Second Order ◽  
Base Space ◽  
Cohomology Groups ◽  
Trivial Bundle ◽  
Cech Cohomology

Abstract Let (E, π, M) be a vector bundle. We define two cohomology groups associated to π using the first and second order jet manifolds of this bundle. We prove that one of them is isomorphic with a Čech cohomology group of the base space. The particular case of trivial bundle is studied

scholarly journals ON GENERALIZED NONHOLONOMIC CHAPLYGIN SPHERE PROBLEM

2013 ◽  
Vol 10 (06) ◽  
pp. 1320008 ◽  
Author(s):  
A. V. TSIGANOV
Keyword(s):  
Poisson Structure ◽  
Nontrivial Deformation

We discuss linear in momenta Poisson structure for the generalized nonholonomic Chaplygin sphere problem and prove that it is nontrivial deformation of the canonical Poisson structure on e*(3).

Cohomology of Flat Principal Bundles

2018 ◽  
Vol 61 (3) ◽  
pp. 869-877
Author(s):  
Yanghyun Byun ◽  
Joohee Kim
Keyword(s):  
Lie Group ◽  
Principal Bundle ◽  
Real Coefficient ◽  
Similar Argument ◽  
Flat Connection ◽  
De Rham Cohomology ◽  
Trivial Bundle ◽  
De Rham ◽  
Adjoint Bundle ◽  
Connected Lie Group

AbstractWe invoke the classical fact that the algebra of bi-invariant forms on a compact connected Lie group G is naturally isomorphic to the de Rham cohomology H*dR(G) itself. Then, we show that when a flat connection A exists on a principal G-bundle P, we may construct a homomorphism EA: H*dR(G)→H*dR(P), which eventually shows that the bundle satisfies a condition for the Leray–Hirsch theorem. A similar argument is shown to apply to its adjoint bundle. As a corollary, we show that that both the flat principal bundle and its adjoint bundle have the real coefficient cohomology isomorphic to that of the trivial bundle.

scholarly journals A generalization of the topological Brauer group

2008 ◽  
Vol 2 (3) ◽  
pp. 407-444 ◽  
Author(s):  
A. V. Ershov
Keyword(s):  
Matrix Algebra ◽  
Structure Group ◽  
Brauer Group ◽  
Trivial Bundle ◽  
Homotopy Invariants

AbstractIn the present paper we study some homotopy invariants which can be defined by means of bundles with fiber being a matrix algebra. In particular, we introduce some generalization of the Brauer group in the topological context and show that any of its elements can be represented as a locally trivial bundle with the structure group,k∈. Finally, we discuss its possible applications in the twistedK-theory.

scholarly journals D-INSTANTON SUMS FOR MATTER HYPERMULTIPLETS

2004 ◽  
Vol 19 (35) ◽  
pp. 2645-2653 ◽  
Author(s):  
SERGEI V. KETOV ◽  
OSVALDO P. SANTILLAN ◽  
ANDREI G. ZORIN
Keyword(s):  
Infinite Number ◽  
Moduli Space ◽  
Quantum Corrections ◽  
The Real ◽  
Nontrivial Deformation

We calculate some nonperturbative (D-instanton) quantum corrections to the moduli space metric of several (n>1) identical matter hypermultiplets for the type-IIA superstrings compactified on a Calabi–Yau threefold, near conifold singularities. We find a nontrivial deformation of the (real) 4n-dimensional hypermultiplet moduli space metric due to the infinite number of D-instantons, under the assumption of n tri-holomorphic commuting isometries of the metric, in the hyper-Kähler limit (i.e. in the absence of gravitational corrections).

Moduli spaces of bundles on an abelian variety

2017 ◽  
Vol 14 (02) ◽  
pp. 1750030
Author(s):  
Indranil Biswas
Keyword(s):  
Algebraic Group ◽  
Abelian Variety ◽  
Moduli Spaces ◽  
Character Variety ◽  
Higgs Bundles ◽  
Connected Component ◽  
Trivial Bundle

Let [Formula: see text] be a complex abelian variety and [Formula: see text] a complex reductive affine algebraic group. We describe the connected component, containing the trivial bundle, of the moduli spaces of topologically trivial principal [Formula: see text]-bundles and [Formula: see text]-Higgs bundles on [Formula: see text]. We also describe the moduli spaces of [Formula: see text]-connections and the [Formula: see text]-character variety for [Formula: see text].

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