We present geometric constructions which realize the local cohomology filtration in the setting of equivariant bordism, with the aim of understanding free $G$ actions on manifolds. We begin by reviewing the basic construction of the local cohomology filtration, starting with the Conner-Floyd tom Dieck exact sequence. We define this filtration geometrically using the language of families of subgroups. We then review Atiyah-Segal-Wilson $K$-theory invariants, which are well-suited for studying the manifolds produced by our techniques. We end by indicating potential applications of these ideas.
Homology, Homotopy and Applications, Vol. 3(2), 2001, pp. 385-406
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