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This paper is an exposition of the relationship between Witten's Chern-Simonsfunctional integral and the theory of Vassiliev Invariants of knots and linksin three dimensional space. We conceptualize the functional integral in termsof equivalence classes of functionals of gauge fields and we do not use measuretheory. This approach makes it possible to discuss the mathematics intrinsic tothe functional integral rigorously and without functional integration.Applications to loop quantum gravity are discussed. We thank the organizers ofthe Conference on 60 Years of Yang-Mills Gauge Field Theories (25 to 28 May2015) for the invitation and opportunity to speak about these ideas inSingapore.

Chern-Simons Theory, Vassiliev Invariants, Loop Quantum Gravity and Functional Integration Without Integration