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3-manifold asymmetric signature boundary braid bundle chain cobordant cofibrant cohomology components compute connected construction Corollary corresponding crossing circle defined Definition denote diffeomorphism differential dimension disk duality edges element embedding equivariant exact sequence external vertices fiber fiberwise fibration Figure finite flip-isomorphism function functors G-invariant given graphs group and let groupoids Hence Hochschild Hochschild cohomology homology groups homomorphism homotopy hyperbolic implies induced integral invariant involution isoa isomorphism isotopy Jacobi diagram Khovanov homology Knot Theory Lemma Let G Lie algebra Lie group linear Math min-geodesic morphism nonzero obtain orientation Poincare duality polynomial proof of Theorem proper smooth Proposition prove Przytycki quadratic Poincaré pair quasi-coherent reduction rules result ribbon Section Seifert surface sheaves simplicial skein modules smooth G manifold smooth G-equivariant stable structure submanifold surgery theory torus knots trivial tubular neighbourhood vector field vertex weak equivalence