Abstract
Let G be the group Z2. Denote byR n,k theR n+k with non trivial G-action on the first n coordinates. Let ɛn,k be the trivial bundle with fibreR n,k. We say that a G-manifold M is (n,k)-framable if t(M)= =ɛn,k in KOG(M) with t(M) the tangent bundle of M. We show that if G acts on a homotopy sphere ∑n+k such that the fixed point set is a k-dimensional homotopy sphere then ∑ is (n,k)-framable.
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Löffler, P. Equivariant framability of involutions on homotopy spheres. Manuscripta Math 23, 161–171 (1978). https://doi.org/10.1007/BF01180571
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DOI: https://doi.org/10.1007/BF01180571