Displaying similar documents to “On manifolds homotopy equivalent to the total spaces of S 7 -bundles over S 8

C*-semigroup bundles and C*-algebras whose irreducible representations are all finite dimensional

Thomas Müller

Similarity:

We investigate the structure of C*-algebras with a finite bound on the dimensions of their irreducible representations, sometimes called “subhomogeneous”.In the first chapter we develop the theory of C*-semigroup bundles. These are C*-bundles over semigroups together with a “structure map” which links the semigroup structure of the base space lo the bundle. Under suitable conditions we prove the existence of “enough” bounded sections, which arc “compatible” with the C*-semigroup bundle...

A classification theorem on Fano bundles

Roberto Muñoz, Luis E. Solá Conde, Gianluca Occhetta (2014)

Annales de l’institut Fourier

Similarity:

In this paper we classify rank two Fano bundles on Fano manifolds satisfying H 2 ( X , ) H 4 ( X , ) . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization ( ) , that allows us to obtain the cohomological invariants of X and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.

Lifts of Foliated Linear Connectionsto the Second Order Transverse Bundles

Vadim V. Shurygin, Svetlana K. Zubkova (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

The second order transverse bundle T 2 M of a foliated manifold M carries a natural structure of a smooth manifold over the algebra 𝔻 2 of truncated polynomials of degree two in one variable. Prolongations of foliated mappings to second order transverse bundles are a partial case of more general 𝔻 2 -smooth foliated mappings between second order transverse bundles. We establish necessary and sufficient conditions under which a 𝔻 2 -smooth foliated diffeomorphism between two second order transverse...

A decomposition of E 3 into straight arcs and singletons

S. Armentrout

Similarity:

CONTENTS1. Introduction............................................................................................................................................. 52. Notation and. terminology................................................................................................................... 63. Description of G.................................................................................................................................... 64. Preliminaries to the...

Line bundles with partially vanishing cohomology

Burt Totaro (2013)

Journal of the European Mathematical Society

Similarity:

Define a line bundle L on a projective variety to be q -ample, for a natural number q , if tensoring with high powers of L kills coherent sheaf cohomology above dimension q . Thus 0-ampleness is the usual notion of ampleness. We show that q -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that q -ampleness is a Zariski open condition, which is not clear from the definition. ...

Linear liftings of affinors to Weil bundles

Jacek Dębecki (2003)

Colloquium Mathematicae

Similarity:

We give a classification of all linear natural operators transforming affinors on each n-dimensional manifold M into affinors on T A M , where T A is the product preserving bundle functor given by a Weil algebra A, under the condition that n ≥ 2.

Minimal component numbers of fixed point sets

Xuezhi Zhao (2003)

Fundamenta Mathematicae

Similarity:

Let f: (X,A) → (X,A) be a relative map of a pair of compact polyhedra. We introduce a new relative homotopy invariant N C ( f ; X , A ) , which is a lower bound for the component numbers of fixed point sets of the self-maps in the relative homotopy class of f. Some properties of N C ( f ; X , A ) are given, which are very similar to those of the relative Nielsen number N(f;X,A).

On weak i -homotopy equivalences of modules

Zheng-Xu He (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

Si definisce il gruppo di i —omotopia di un singolo modulo e si introduce la nozione di equivalenza i -omotopica debole. Sotto determinate condizioni per l'anello di base Λ oppure per i moduli considerati, le equivalenze i -omotopiche deboli coincidono con le equivalenze i -omotopiche (forti).

Pseudo-real principal Higgs bundles on compact Kähler manifolds

Indranil Biswas, Oscar García-Prada, Jacques Hurtubise (2014)

Annales de l’institut Fourier

Similarity:

Let X be a compact connected Kähler manifold equipped with an anti-holomorphic involution which is compatible with the Kähler structure. Let G be a connected complex reductive affine algebraic group equipped with a real form σ G . We define pseudo-real principal G -bundles on X . These are generalizations of real algebraic principal G -bundles over a real algebraic variety. Next we define stable, semistable and polystable pseudo-real principal G -bundles. Their relationships with the usual...

G-functors, G-posets and homotopy decompositions of G-spaces

Stefan Jackowski, Jolanta Słomińska (2001)

Fundamenta Mathematicae

Similarity:

We describe a unifying approach to a variety of homotopy decompositions of classifying spaces, mainly of finite groups. For a group G acting on a poset W and an isotropy presheaf d:W → (G) we construct a natural G-map h o c o l i m d G / d ( - ) | W | which is a (non-equivariant) homotopy equivalence, hence h o c o l i m d E G × G F d E G × G | W | is a homotopy equivalence. Different choices of G-posets and isotropy presheaves on them lead to homotopy decompositions of classifying spaces. We analyze higher limits over the categories associated to isotropy...

Real algebraic actions on projective spaces - A survey

Ted Petrie (1973)

Annales de l'institut Fourier

Similarity:

Let G be a compact lie group. We introduce the set S G ( Y ) for every smooth G manifold Y . It consists of equivalence classes of pair ( X , f ) where f : X Y is a G map which defines a homotopy equivalence from X to Y . Two pairs ( X i , f i ) , for i = 0 , 1 , are equivalent if there is a G homotopy equivalence φ : X 0 X 1 such that f 0 is G homotopic to f 1 φ . Properties of the set S G ( Y ) and related to the representation of G on the tangent spaces of X and Y at the fixed points. For the case G = S 1 and Y is the S 1 manifold defined by a “linear”...

Lifting to the r-frame bundle by means of connections

J. Kurek, W. M. Mikulski (2010)

Annales Polonici Mathematici

Similarity:

Let m and r be natural numbers and let P r : f m be the rth order frame bundle functor. Let F : f m and G : f k be natural bundles, where k = d i m ( P r m ) . We describe all f m -natural operators A transforming sections σ of F M M and classical linear connections ∇ on M into sections A(σ,∇) of G ( P r M ) P r M . We apply this general classification result to many important natural bundles F and G and obtain many particular classifications.

Homotopy invariance of higher signatures and 3 -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

Similarity:

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3 -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable 3 -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...

Singular principal G -bundles on nodal curves

Alexander Schmitt (2005)

Journal of the European Mathematical Society

Similarity:

In the present paper, we give a first general construction of compactified moduli spaces for semistable G -bundles on an irreducible complex projective curve X with exactly one node, where G is a semisimple linear algebraic group over the complex numbers.

Correction for the paper “ S 3 -bundles and exotic actions”

T. E. Barros (2001)

Bulletin de la Société Mathématique de France

Similarity:

In [R] explicit representatives for S 3 -principal bundles over S 7 are constructed, based on these constructions explicit free S 3 -actions on the total spaces are described, with quotients exotic 7 -spheres. To describe these actions a classification formula for the bundles is used. This formula is not correct. In Theorem 1 below, we correct the classification formula and in Theorem 2 we exhibit the correct indices of the exotic 7 -spheres that occur as quotients of the free S 3 -actions described...

On the homotopy transfer of A structures

Jakub Kopřiva (2017)

Archivum Mathematicum

Similarity:

The present article is devoted to the study of transfers for A structures, their maps and homotopies, as developed in [7]. In particular, we supply the proofs of claims formulated therein and provide their extension by comparing them with the former approach based on the homological perturbation lemma.

Singular Bundles with Bounded L 2 -Curvatures

Thiemo Kessel, Tristan Rivière (2008)

Bollettino dell'Unione Matematica Italiana

Similarity:

We consider calculus of variations of the Yang-Mills functional in dimensions larger than the critical dimension 4. We explain how this naturally leads to a class of - a priori not well-defined - singular bundles including possibly "almost everywhere singular bundles". In order to overcome this difficulty, we suggest a suitable new framework, namely the notion of singular bundles with bounded L 2 -curvatures.