@MISC{Manifolds_jeffrey-weitsman-witteninvariants, author = {Seifert Fibred Manifolds}, title = {JEFFREY-WEITSMAN-WITTEN INVARIANTS OF}, year = {} }

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Abstract

Abstract. We introduce a result in [4] about Jeffrey-Weitsman-Witten invariants of Seifert fibred manifolds. 1. Definition of Jeffrey-Weitsman-Witten invariant We review the Chern-Simons gauge theory to understand the definition of the Jeffrey-Weitsman-Witten invariant. For the detail of the Chern-Simons gauge theory, see [5], [3]. Let X be a 2-dimensional manifold and P be a principal SU(2)-bundle over X. Let A,AF,G be the affine space of connection one forms of P, the space of flat connections of P and the gauge transformation group of P respectively. Let M2 be the moduli space of the flat connections of P. We consider a 3-dimensional manifold Y1 with a boundary X. Moreover we assume that a neighborhood of X in Y1 is diffeomorphic to X × [0, 1). For A ∈ A, g ∈ G we consider a U(1)-valued function S(A, g) defined by (1) S(A, g) ≡ exp(2pii(CS(Ãg̃) − CS(Ã))) where A ̃ and g ̃ are the extensions of A and g into Y1, Ãg ̃ is the gauge transformation of A ̃ by g ̃ and the Chern-Simons invariant CS(Ã) is given by