Extended moduli spaces and the Kan construction.II.Lattice gauge theory
| dc.creator | Huebschmann, Johannes | |
| dc.date | 1995-06-14 | |
| dc.date.accessioned | 2026-07-07T09:12:33Z | |
| dc.date.available | 2026-07-07T09:12:33Z | |
| dc.description | Let $Y$ 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.description | AMSTeX 2.1, 21 pages | |
| dc.identifier | https://arxiv.org/abs/dg-ga/9506006 | |
| dc.identifier | http://arxiv.org/abs/dg-ga/9506006 | |
| dc.identifier | Topology 38 (1999) 555-596 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152058 | |
| dc.subject | Differential Geometry | |
| dc.title | Extended moduli spaces and the Kan construction.II.Lattice gauge theory | |
| dc.type | text |