Extended moduli spaces and the Kan construction.II.Lattice gauge theory

dc.creatorHuebschmann, Johannes
dc.date1995-06-14
dc.date.accessioned2026-07-07T09:12:33Z
dc.date.available2026-07-07T09:12:33Z
dc.descriptionLet $Y$ be a CW-complex with a single 0-cell, $K$ its Kan group, a model for the loop space of $Y$, and let $G$ be a compact, connected Lie group. We give an explicit finite dimensional construction of generators of the equivariant cohomology of the geometric realization of the cosimplicial manifold $\roman{Hom}(K,G)$ and hence of the space $\roman{Map}^o(Y,BG)$ of based maps from $Y$ to the classifying space $BG$. For a smooth manifold $Y$, this may be viewed as a rigorous approach to lattice gauge theory, and we show that it then yields, (i) when {$\roman{dim}(Y)=2$,} equivariant de Rham representatives of generators of the equivariant cohomology of twisted representation spaces of the fundamental group of a closed surface including generators for moduli spaces of semi stable holomorphic vector bundles on complex curves so that, in particular, the known structure of a stratified symplectic space results; (ii) when {$\roman{dim}(Y)=3$,} equivariant cohomology generators including the Chern-Simons function; (iii) when {$\roman{dim}(Y) = 4$,} the generators of the relevant equivariant cohomology from which for example Donaldson polynomials are obtained by evaluation against suitable fundamental classes corresponding to moduli spaces of ASD connections.
dc.descriptionAMSTeX 2.1, 21 pages
dc.identifierhttps://arxiv.org/abs/dg-ga/9506006
dc.identifierhttp://arxiv.org/abs/dg-ga/9506006
dc.identifierTopology 38 (1999) 555-596
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152058
dc.subjectDifferential Geometry
dc.titleExtended moduli spaces and the Kan construction.II.Lattice gauge theory
dc.typetext

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