On p-local homotopy types of gauge groups

2014 ◽  
Vol 144 (1) ◽  
pp. 149-160 ◽  
Author(s):  
Daisuke Kishimoto ◽  
Akira Kono ◽  
Mitsunobu Tsutaya
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Principal Bundle ◽  
Dimensional Sphere ◽  
Gauge Groups ◽  
Homotopy Types

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.

Unstable K1-group and homotopy type of certain gauge groups

2006 ◽  
Vol 136 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Hiroaki Hamanaka ◽  
Akira Kono
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Complete Classification ◽  
Necessary Condition ◽  
Gauge Groups ◽  
Homotopy Types

We denote the group of homotopy set [X, U(n)] by the unstable K1-group of X. In this paper, using the unstable K1-group of the multi-suspended CP2, we give a necessary condition for two principal SU(n)-bundles over §4 to have the associated gauge group of the same homotopy type, which is an improvement of the result of Sutherland and, particularly, show the complete classification of homotopy types of SU(3)-gauge groups over S4.

A note on the homotopy type of certain gauge groups

1991 ◽  
Vol 117 (3-4) ◽  
pp. 295-297 ◽  
Author(s):  
Akira Kono
Keyword(s):  
Gauge Group ◽  
Homotopy Type ◽  
Gauge Groups

SynopsisLet Gk be the gauge group of Pk, the principal SU(2) bundle over S4 with c2(Pk) = k. In this paper we show that Gk ≃ Gk. if and only if (12, k) = (12, k′) where (12, k) is the GCD of 12 and k.

scholarly journals CONTINUOUS TRACE C*-ALGEBRAS, GAUGE GROUPS AND RATIONALIZATION

2009 ◽  
Vol 01 (03) ◽  
pp. 261-288 ◽  
Author(s):  
JOHN R. KLEIN ◽  
CLAUDE L. SCHOCHET ◽  
SAMUEL B. SMITH
Keyword(s):  
Gauge Group ◽  
Metric Space ◽  
Principal Bundle ◽  
Rational Homotopy ◽  
Compact Metric Space ◽  
Gauge Groups ◽  
C Algebra ◽  
C Algebras ◽  
Rational Cohomology ◽  
Rational Homotopy Type

Let ζ be an n-dimensional complex matrix bundle over a compact metric space X and let Aζdenote the C*-algebra of sections of this bundle. We determine the rational homotopy type as an H-space of UAζ, the group of unitaries of Aζ. The answer turns out to be independent of the bundle ζ and depends only upon n and the rational cohomology of X. We prove analogous results for the gauge group and the projective gauge group of a principal bundle over a compact metric space X.

scholarly journals Gauge groups and bialgebroids

2021 ◽  
Vol 111 (6) ◽  
Author(s):  
Xiao Han ◽  
Giovanni Landi
Keyword(s):  
Gauge Group ◽  
Galois Extension ◽  
Principal Bundle ◽  
Module Structure ◽  
Crossed Module ◽  
Gauge Groups ◽  
Quantum Sphere ◽  
Hopf Algebroid ◽  
Commutative Algebras

AbstractWe study the Ehresmann–Schauenburg bialgebroid of a noncommutative principal bundle as a quantization of the gauge groupoid of a classical principal bundle. We show that the gauge group of the noncommutative bundle is isomorphic to the group of bisections of the bialgebroid, and we give a crossed module structure for the bisections and the automorphisms of the bialgebroid. Examples include: Galois objects of Taft algebras, a monopole bundle over a quantum sphere and a not faithfully flat Hopf–Galois extension of commutative algebras. For each of the latter two examples, there is in fact a suitable invertible antipode for the bialgebroid making it a Hopf algebroid.

scholarly journals HOMOTOPY TYPES OF GAUGE GROUPS OVER NON-SIMPLYCONNECTED CLOSED 4-MANIFOLDS

2018 ◽  
Vol 61 (2) ◽  
pp. 349-371 ◽  
Author(s):  
TSELEUNG SO
Keyword(s):  
Homotopy Type ◽  
Lie Group ◽  
Compact Lie Group ◽  
Gauge Groups ◽  
Homotopy Types ◽  
Simply Connected

AbstractLet G be a simple, simply connected, compact Lie group, and let M be an orientable, smooth, connected, closed 4-manifold. In this paper, we calculate the homotopy type of the suspension of M and the homotopy types of the gauge groups of principal G-bundles over M when π1(M) is (1) ℤ*m, (2) ℤ/prℤ, or (3) ℤ*m*(*nj=1ℤ/prjjℤ), where p and the pj's are odd primes.

Homotopy invariants and continuous mappings

1950 ◽  
Vol 202 (1069) ◽  
pp. 253-263 ◽  
Keyword(s):  
Homotopy Type ◽  
Betti Numbers ◽  
Continuous Mappings ◽  
Numerical Invariants ◽  
Homotopy Invariants

This paper contributes new numerical invariants to the topology of a certain class of polyhedra. These invariants, together with the Betti numbers and coefficients of torsion, characterize the homotopy type of one of these polyhedra. They are also applied to the classification of continuous mappings of an ( n + 2)-dimensional polyhedron into an ( n + 1)-sphere ( n > 2).

scholarly journals COMBINATORIAL AND TOPOLOGICAL PHASE STRUCTURE OF NON-PERTURBATIVE n-DIMENSIONAL QUANTUM GRAVITY

1992 ◽  
Vol 06 (11n12) ◽  
pp. 2109-2121
Author(s):  
M. CARFORA ◽  
M. MARTELLINI ◽  
A. MARZUOLI
Keyword(s):  
Quantum Gravity ◽  
Phase Structure ◽  
Gravity Models ◽  
Topological Phase ◽  
Geometrical Characterization ◽  
Homotopy Types ◽  
Geometrical Constraints ◽  
Riemannian Geometries

We provide a non-perturbative geometrical characterization of the partition function of ndimensional quantum gravity based on a rough classification of Riemannian geometries. We show that, under natural geometrical constraints, the theory admits a continuum limit with a non-trivial phase structure parametrized by the homotopy types of the class of manifolds considered. The results obtained qualitatively coincide, when specialized to dimension two, with those of two-dimensional quantum gravity models based on random triangulations of surfaces.

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