TANGENTIAL REPRESENTATIONS AT ISOLATED FIXED POINTS OF ODD-DIMENSIONAL G-MANIFOLDS
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초록
Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the xed point set M G ≠φ and dim M G = 0, then G has a subgroup H with G/H ∼= Z₂, the cyclic groupof order 2. The tangential representation γx (M ) of G at x ∈M G is alsoregarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.
Abstract
Let G be a compact abelian Lie group, and M an odd-dimensional closed smooth G-manifold. If the xed point set M G ≠φ and dim M G = 0, then G has a subgroup H with G/H ∼= Z₂, the cyclic groupof order 2. The tangential representation γx (M ) of G at x ∈M G is alsoregarded as a representation of H by restricted action. We show that the number of fixed points is even, and that the tangential representations at fixed points are pairwise isomorphic as representations of H.
참고문헌 (5)
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