## Algebraic & Geometric Topology: AGT. |

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3-manifolds action Adams operations annulus assume automorphism bigons blue double curve boundary components bundle chain algebra classifying space coalgebra cohomology colimit compact group compute connected contains Corollary curves with triple defined Definition denote differential disjoint elementary abelian elements epimorphism essential blue exact sequence fiber fibration Figure finite group follows functor fundamental group fusion system green arcs green double curve green strip hence hexagons homology homomorphism homotopy equivalence Hopf algebra implies induced inessential curves inner solid torus integer intersection invariant irreducible isomorphism knot Lemma lens space manifold mapping class groups Math module monoid morphism nontrivial obtain operad orbit orientation outer solid torus p-compact pair polynomial prime Proposition quotient red arcs red torus result saddle arc Section simplicial solid torus spectral sequence structure subgroup surface surgery sweepout Sylow Sylow subgroup topological triple points trivial unstable Adams operations vector Weyl group