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Circle Actions on 3Manifolds
Resolution of Singularities
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3-dimensional 3-manifold action of G algebraic analytic automorphism bundle over S1 called characteristic map closed 3-manifold commutative compact complex cross-section curve cyclic group defined denote diffeomorphic E-orbit element equivariant equivariant resolution equivariant sewing fibers over S1 fibration finite fundamental group finite groups finite number finite subgroup fixed point free foliation fundamental groups G-vector bundle genus given graph group G homeomorphism induced integer irreducible isolated singularity isomorphism isotropy group large Seifert manifolds left rotation Lemma lens spaces Let G linear matrix monoidal transform morphism non-orientable non-singular non-trivial normal bundle normal subgroup Note obtained open set orbit invariants orbit space orthogonal plumbing principal orbit Proof quotient relatively prime result S1-action satisfying Seifert bundle Seifert invariants Seifert manifolds singular point slice smooth manifold solid torus structure group subset surface Theorem topological total space transform with center trivial Waldhausen weighted homogeneous weighted homogeneous polynomial zero section