Homotopy types of $${{\textrm{Spin}}}^{{\textrm{c}}}(n)$$-gauge groups over $$S^4$$

Homotopy, monopoles and ’t Hooft tensor for generic gauge groups

We study monopoles and corresponding ’t Hooft tensor in a generic gauge theory. This issue is relevant to the understanding of the color confinement in terms of dual symmetry.

Computing Homotopy Types Using Crossed N -cubes of Groups∗

The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some cases completely computable, in a way not possible with the traditional Postnikov systems, or with other models, such as simplicial groups. These algebraic st...

Homotopy Types

For an arbitrary simplicial complex K, Davis and Januszkiewicz have defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to Davis and Januszkiewicz’s examples. It is therefore natural to investigate t...

Antisymmetric Tensor Gauge Fields on S4

Homotopy Groups of Compact Abelian Groups

Preliminaries. Bn (resp. 5„_i) will denote the subset of Rn consisting of those x such that ||x|| g 1 (resp. ¡|x|| = 1). x0 will denote the point (1, 0, 0, •• -, 0) of R" and T will denote Si made into a topological group by using complex multiplication. All groups will be assumed to be Abelian. For a based topological space X and a topological group G, let C(X, G) denote the set of maps (i.e.,...