Homotopy Types Of Gauge Groups Research Articles

Homotopy types of gauge groups over Riemann surfaces

Homotopy types of gauge groups over Riemann surfaces

The homotopy type of a once-suspended 6-manifold and its applications

Let M be a closed, oriented, simply connected 6-manifold. After localization away from 2, we give a homotopy decomposition of ΣM in terms of spheres, Moore spaces and other recognizable spaces. As applications we calculate generalized cohomology groups of M and determine the homotopy types of gauge groups of certain bundles over M.

The homotopy types of mathrm{SO}(4)-gauge groups

The homotopy types of gauge groups of principal mathrm{SO}(4)-bundles over S^{4} are classified p-locally for every prime p, and partial results are obtained integrally. The method generalizes to deal with any quotient of the form (S^{3})^{n}/Z where Z is a subgroup generated by (-1,ldots ,-1).

The homotopy types of U(n)-gauge groups over lens spaces

We analyse the homotopy types of gauge groups for principal U(n)-bundles over lens spaces and two-dimensional Moore spaces.

Homotopy types of gauge groups of mathrm {PU}(p)-bundles over spheres

We examine the relation between the gauge groups of mathrm {SU}(n)- and mathrm {PU}(n)-bundles over S^{2i}, with 2le ile n, particularly when n is a prime. As special cases, for mathrm {PU}(5)-bundles over S^4, we show that there is a rational or p-local equivalence mathcal {G}_{2,k}simeq _{(p)}mathcal {G}_{2,l} for any prime p if, and only if, (120,k)=(120,l), while for mathrm {PU}(3)-bundles over S^6 there is an integral equivalence mathcal {G}_{3,k}simeq mathcal {G}_{3,l} if, and only if, (120,k)=(120,l).

Homotopy types of gauge groups related to S3-bundles over S4

Let Ml,m be the total space of the S3-bundle over S4 classified by the element lσ+mρ∈π4(SO(4)), l,m∈Z. In this paper we study the homotopy theory of gauge groups of principal G-bundles over manifolds Ml,m when G is a simply connected simple compact Lie group such that π6(G)=0. That is, G is one of the following groups: SU(n)(n≥4), Sp(n)(n≥2), Spin(n)(n≥5), F4, E6, E7, E8. If the integral homology of Ml,m is torsion-free, we describe the homotopy type of the gauge groups over Ml,m as products of recognisable spaces. For any manifold Ml,m with non-torsion-free homology, we give a p-local homotopy decomposition, for a prime p≥5, of the loop space of the gauge groups.

Odd primary homotopy types of the gauge groups of exceptional Lie groups

The p-local homotopy types of gauge groups of principal G-bundles over S^4 are classified when G is a compact connected exceptional Lie group without p-torsion in homology except for (G,p) = (E7,5).

Homotopy decompositions of gauge groups over real surfaces

We analyse the homotopy types of gauge groups of principal U(n)-bundles associated to pseudo Real vector bundles in the sense of Atiyah. We provide satisfactory homotopy decompositions of these gauge groups into factors in which the homotopy groups are well known. Therefore, we substantially build upon the low dimensional homotopy groups as provided in a paper by I. Biswas, J. Huisman, and J. Hurtubise.

On p-local homotopy types of gauge groups

The aim of this paper is to show that the p-local homotopy type of the gauge group of a principal bundle over an even-dimensional sphere is completely determined by the divisibility of the classifying map by p. In particular, for gauge groups of principal SU(n)-bundles over S2d for 2 ≤ d ≤ p − 1 and n ≤ 2p − 1, we give a concrete classification of their p-local homotopy types.

Modpdecompositions of gauge groups

We give mod p decompositions of homotopy types of the gauge groups of principal bundles over spheres, which are compatible with mod p decompositions of Lie groups given by Mimura, Nishida and Toda. As an application, we also give some computations on the homotopy types of gauge groups. In particular, we show the p–local converse of the result of Sutherland on the classifications of the gauge groups of principal SU.n/–bundles.

The homotopy types of gauge groups of nonorientable surfaces and applications to moduli spaces

We determine the homotopy types of gauge groups of principle $G$-bundles over closed, connected nonorientable surfaces for $G=U(n)$ and $G$ a simply-connected, compact Lie group. Applications are made to moduli spaces of stable vector bundles.

Counting Homotopy Types of Gauge Groups

For K a connected finite complex and G a compact connected Lie group, a finiteness result is proved for gauge groups G(P) of principal G-bundles P over K: as P ranges over all principal G-bundles with base K, the number of homotopy types of G(P) is finite; indeed this remains true when these gauge groups are classified by H-equivalence, that is, homotopy equivalences which respect multiplication up to homotopy. A case study is given for K = S4, G = SU(2): there are eighteen H-equivalence classes of gauge group in this case. These questions are studied via fibre homotopy theory of bundles of groups; the calculations in the case study involve K-theories and e-invariants. 1991 Mathematics Subject Classification: 54C35, 55P15, 55R10.