scholarly journals Transversality for the moduli space of Spin(7)-instantons

2019 ◽  
Vol 32 (05) ◽  
pp. 2050013
Author(s):  
Vicente Muñoz ◽  
C. S. Shahbazi
Keyword(s):  
Vector Bundle ◽  
Moduli Space ◽  
Dimensional Manifold ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Integrable Spin

We construct the moduli space of Spin(7)-instantons on a hermitian complex vector bundle over a closed 8-dimensional manifold endowed with a (possibly non-integrable) Spin(7)-structure. We find suitable perturbations that achieve regularity of the moduli space, so that it is smooth and of the expected dimension over the irreducible locus.

A REMARK ON THE STABLE REAL FORMS OF COMPLEX VECTOR BUNDLES OVER MANIFOLDS

2017 ◽  
Vol 96 (1) ◽  
pp. 69-76
Author(s):  
HUIJUN YANG
Keyword(s):  
Vector Bundle ◽  
Smooth Manifold ◽  
Vector Bundles ◽  
Characteristic Classes ◽  
Dimensional Manifold ◽  
Real Form ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Simply Connected ◽  
Real Forms

Let$M$be an$n$-dimensional closed oriented smooth manifold with$n\equiv 4\;\text{mod}\;8$, and$\unicode[STIX]{x1D702}$be a complex vector bundle over$M$. We determine the final obstruction for$\unicode[STIX]{x1D702}$to admit a stable real form in terms of the characteristic classes of$M$and$\unicode[STIX]{x1D702}$. As an application, we obtain the criteria to determine which complex vector bundles over a simply connected four-dimensional manifold admit a stable real form.

scholarly journals First Chern class and holomorphic tensor fields

1980 ◽  
Vol 77 ◽  
pp. 5-11 ◽  
Author(s):  
Shoshichi Kobayashi
Keyword(s):  
Vector Bundle ◽  
Cotangent Bundle ◽  
Symmetric Tensor ◽  
Complex Vector Bundle ◽  
Tensor Fields ◽  
Kaehler Manifold ◽  
Complex Vector ◽  
Tensor Power ◽  
Holomorphic Sections ◽  
First Chern Class

Let M be an n-dimensional compact Kaehler manifold, TM its (holomorphic) tangent bundle and T*M its cotangent bundle. Given a complex vector bundle E over M, we denote its m-th symmetric tensor power by SmE and the space of holomorphic sections of E by Γ(E).

Splitting ℂP∞ and Bℤ/pn into Thom spectra

1989 ◽  
Vol 106 (2) ◽  
pp. 263-271 ◽  
Author(s):  
Brayton Gray ◽  
Nigel Ray
Keyword(s):  
Vector Bundle ◽  
Algebraic Topology ◽  
Steenrod Algebra ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Thom Spectra ◽  
Stable Splitting ◽  
Image Position

In recent years, much work in algebraic topology has been devoted to stable splitting phenomena. Often the existence of these splittings has first been detected at the cohomological level in terms of modules over the Steenrod algebra.For example, W. Richter has exhibited a decomposition of ΩSU(n) of the form(see [7]). Not only were cohomology calculations the initial evidence for this situation, but they further suggested that each summand Gk might be the Thom complex of a suitable k-plane complex vector bundle. This possibility was also verified by Mitchell.

Holomorphic Frames for Weakly Converging Holomorphic Vector Bundles

2006 ◽  
Vol 49 (1) ◽  
pp. 36-40 ◽  
Author(s):  
Georgios D. Daskalopoulos ◽  
Richard A. Wentworth
Keyword(s):  
Vector Bundle ◽  
Complex Manifold ◽  
Vector Bundles ◽  
Convergent Sequence ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Hölder Class ◽  
Holomorphic Vector Bundles ◽  
Holder Class

AbstractUsing a modification of Webster's proof of the Newlander–Nirenberg theorem, it is shown that, for a weakly convergent sequence of integrable unitary connections on a complex vector bundle over a complex manifold, there is a subsequence of local holomorphic frames that converges strongly in an appropriate Holder class.

On the Kunneth formula spectral sequence in equivariant K- theory

1972 ◽  
Vol 72 (2) ◽  
pp. 167-177 ◽  
Author(s):  
V. P. Snaith
Keyword(s):  
Vector Bundle ◽  
Spectral Sequence ◽  
Lie Group ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Kunneth Formula ◽  
K Theory ◽  
Torsion Free ◽  
Connected Lie Group

Let G be a compact, connected Lie group such that π2(G) is torsion free. Throughout this paper a vector bundle (representation) will mean a complex vector bundle (representation) and KG will denote the equivariant K-theory functor associabed with the group, G.

scholarly journals On Chern classes of stably fibre homotopic trivial bundles

1988 ◽  
Vol 30 (2) ◽  
pp. 213-214 ◽  
Author(s):  
L. Astey ◽  
S. Gitler ◽  
E. Micha ◽  
G. Pastor
Keyword(s):  
Vector Bundle ◽  
Classical Result ◽  
Chern Classes ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Complex Cobordism ◽  
Stable Cohomology ◽  
Cohomology Operations

Let ξ be a stably fibre homotopic trivial vector bundle. A classical result of Thorn states that the Stiefel-Whitney classes of ξ vanish, and one way to prove this is as follows. Letube the Thorn class of ξ in mod 2 cohomology. Thenuis stably spherical by [2] and therefore all stable cohomology operations vanish onu, showing thatwi(ξ)u= Sqiu= 0. In this note we shall apply this same method using complex cobordism and Landweber-Novikov operations to study relations among Chern classes of a stably fibre homotopic trivial complex vector bundle. We will thus obtain in a unified way certain strong modpconditions for every primep.

scholarly journals On the Cohomology of the Classifying Spaces of Projective Unitary Groups

2019 ◽  
pp. 1-39 ◽  
Author(s):  
Xing Gu
Keyword(s):  
Vector Bundle ◽  
Ring Structure ◽  
Unitary Groups ◽  
Complex Line ◽  
Classifying Spaces ◽  
Complex Vector Bundle ◽  
Primitive Elements ◽  
Complex Vector ◽  
Classifying Space ◽  
Serre Spectral Sequence

Let [Formula: see text] be the classifying space of [Formula: see text], the projective unitary group of order [Formula: see text], for [Formula: see text]. We use a Serre spectral sequence to determine the ring structure of [Formula: see text] up to degree [Formula: see text], as well as a family of distinguished elements of [Formula: see text], for each prime divisor [Formula: see text] of [Formula: see text]. We also study the primitive elements of [Formula: see text] as a comodule over [Formula: see text], where the comodule structure is given by an action of [Formula: see text] on [Formula: see text] corresponding to the action of taking the tensor product of a complex line bundle and an [Formula: see text]-dimensional complex vector bundle.

On complex vector bundles on rational threefolds

1985 ◽  
Vol 97 (2) ◽  
pp. 279-288 ◽  
Author(s):  
Constantin BẮnicẮ ◽  
Mihai Putinar
Keyword(s):  
Vector Bundle ◽  
Algebraic Structure ◽  
Vector Bundles ◽  
Topological Type ◽  
Rational Surface ◽  
Chern Classes ◽  
Complex Vector Bundle ◽  
Complex Vector ◽  
Algebraic Vector ◽  
Rank 2

It is known [14] that every topological complex vector bundle on a smooth rational surface admits an algebraic structure. In [10] one constructs algebraic vector bundles of rank 2 on with arbitrary Chern classes c1, c2 subject to the necessary topological condition c1 c2 = 0 (mod 2). However, in dimensions greater than 2 the Chern classes don't determine the topological type of a vector bundle. In [2] one classifies the topological complex vector bundles of rank 2 on and one proves that any such bundle admits an algebraic structure.

scholarly journals THE SPACE OF HYPERKÄHLER METRICS ON A 4-MANIFOLD WITH BOUNDARY

2017 ◽  
Vol 5 ◽  
Author(s):  
JOEL FINE ◽  
JASON D. LOTAY ◽  
MICHAEL SINGER
Keyword(s):  
Boundary Value Problem ◽  
Moduli Space ◽  
Dimensional Manifold ◽  
Gravitational Instantons ◽  
Infinite Dimensional ◽  
Manifold With Boundary ◽  
Isometric Actions ◽  
Infinitesimal Deformations ◽  
Hyperkähler Metrics ◽  
Infinite Dimensional Manifold

Let $X$ be a compact 4-manifold with boundary. We study the space of hyperkähler triples $\unicode[STIX]{x1D714}_{1},\unicode[STIX]{x1D714}_{2},\unicode[STIX]{x1D714}_{3}$ on $X$, modulo diffeomorphisms which are the identity on the boundary. We prove that this moduli space is a smooth infinite-dimensional manifold and describe the tangent space in terms of triples of closed anti-self-dual 2-forms. We also explore the corresponding boundary value problem: a hyperkähler triple restricts to a closed framing of the bundle of 2-forms on the boundary; we identify the infinitesimal deformations of this closed framing that can be filled in to hyperkähler deformations of the original triple. Finally we study explicit examples coming from gravitational instantons with isometric actions of $\text{SU}(2)$.

PARABOLIC VECTOR BUNDLES AND HERMITIAN-YANG-MILLS CONNECTIONS OVER A RIEMANN SURFACE

1993 ◽  
Vol 04 (03) ◽  
pp. 467-501 ◽  
Author(s):  
JONATHAN A. PORITZ
Keyword(s):  
Riemann Surface ◽  
Vector Bundle ◽  
Sobolev Space ◽  
Moduli Space ◽  
Vector Bundles ◽  
Weighted Sobolev Space ◽  
Conjugacy Classes ◽  
Stable Bundle ◽  
Yang Mills ◽  
Parabolic Bundles

We study a certain moduli space of irreducible Hermitian-Yang-Mills connections on a unitary vector bundle over a punctured Riemann surface. The connections used have non-trivial holonomy around the punctures lying in fixed conjugacy classes of U (n) and differ from each other by elements of a weighted Sobolev space; these connections give rise to parabolic bundles in the sense of Mehta and Seshadri. We show in fact that the moduli space of stable parabolic bundles can be identified with our moduli space of HYM connections, by proving that every stable bundle admits a unique unitary gauge orbit of Hermitian-Yang-Mills connections.

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