On the Existence of Equivariant Embeddings of Principal Bundles into Vector Bundles
Copyright policy )On the Existence of Equivariant Embeddings of Principal Bundles into Vector Bundles
Let G G be a finite group and let X X be, say, a connected CW-complex of dimension k ⩾ 1 k \geqslant 1 . Let π : E → X \pi :E \to X be a principal G G -bundle and p : V → X p:V \to X an m m -dimensional G G -vector-bundle with trivial action of G G on X X . By an equivariant embedding of π \pi into p p we understand an equivariant embedding h : E → V h:E \to V commuting with projections. We prove a general embedding theorem, a main special case of which is the following Theorem. If k > m k > m and if the action of G G on V V is free outside the zero section for p p , then any principal G G -bundle π : E → X \pi :E \to X can be embedded equivariantly into p : V → X p:V \to X .
equivariant embeddings of principal bundles into vector bundles, Sphere bundles and vector bundles in algebraic topology, Finite transformation groups, Covering spaces and low-dimensional topology, Equivariant fiber spaces and bundles in algebraic topology, Low-dimensional topology of special (e.g., branched) coverings, principal coverings
equivariant embeddings of principal bundles into vector bundles, Sphere bundles and vector bundles in algebraic topology, Finite transformation groups, Covering spaces and low-dimensional topology, Equivariant fiber spaces and bundles in algebraic topology, Low-dimensional topology of special (e.g., branched) coverings, principal coverings
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