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In this paper, we show that the gauge group of a principal P U (n) -bundle over a compact Riemann surface decomposes up to homotopy as the product of factors, one of which is a corresponding gauge group for S 2 and the others are immediately recognizable spaces. Further, when n is a prime p , the gauge group for S 2 decomposes as a product of immediately recognizable factors. These gauge groups have strong connections to moduli spaces of stable vector bundles. [ABSTRACT FROM AUTHOR]

The equivalence class of a principal G 2 -bundle over S 4 is classified by the value k ∈ Z of the second Chern class. In this paper we consider the homotopy types of the corresponding gauge groups G k , and determine the number of homotopy types up to one factor of 2. [ABSTRACT FROM AUTHOR]

Abstract: We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if is a shifted simplicial complex on vertices, are pointed connected -complexes and is the cone on , then the polyhedral product determined by and the pairs is homotopy equivalent to a wedge of suspensions of smashes of the ’s. Earlier work of the authors dealt with the special case where each is a loop space. New techniques are introduced to prove the general case. These have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes. We discuss connections between polyhedral products and toric topology, combinatorics, and classical homotopy theory. [Copyright &y& Elsevier]

For a prime p, the gauge group of a principal U(p)-bundle over a compact, orientable Riemann surface is decomposed up to homotopy as a product of spaces, each of which is commonly known. This is used to deduce explicit computations of the homotopy groups of the moduli space of stable vector bundles through a range, answering a question of Daskalopoulos and Uhlenbeck. [ABSTRACT FROM AUTHOR]

Abstract: The homotopy type of the complement of a complex coordinate subspace arrangement is studied by utilising some connections between its topological and combinatorial structures. A family of arrangements for which the complement is homotopy equivalent to a wedge of spheres is described. One consequence is an application in commutative algebra: certain local rings are proved to be Golod, that is, all Massey products in their homology vanish. [Copyright &y& Elsevier]