2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144468We give an a priori construction of the two-dimensional reduction of three-dimensional quantum Chern-Simons theory. This reduction is a two-dimensional topological quantum field theory and so determines to a Frobenius ring, which here is the twisted equivariant K-theory of a compact Lie group. We construct the theory via correspondence diagrams of moduli spaces, which we "linearize" using complex K-theory. A key point in the construction is to consistently orient these moduli spaces to define pushforwards; the consistent orientation induces twistings of complex K-theory. The Madsen-Tillmann spectra play a crucial role.21 pages, dedicated to Nigel Hitchin on the occasion of his 60th birthday. Version 2 for publication has additional text in section 3 and makes minor correctionsAlgebraic TopologyHigh Energy Physics - TheoryMathematical PhysicsK-Theory and Homologytext