[rho]-compact groups as framed manifolds
Author(s)Bauer, Tilman, 1973-
Massachusetts Institute of Technology. Dept. of Mathematics.
Michael J. Hopkins.
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We describe a natural way to associate to any [rho]-compact group an element of the [rho]-local stable stems, which, applied to the [rho]-completion of a compact Lie group G, coincides with the element represented by the manifold G with its left-invariant framing. To this end, we construct a d-dimensional sphere SG with a stable G-action for every d-dimensional [rho]-compact group G, which generalizes the one-point compactification of the Lie algebra of a Lie group. The homotopy class represented by G is then constructed by means of a transfer map between the Thom spaces of spherical fibrations over BG associated with SG.
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2002.In title on t.p. "[rho]" appears as the lower-case Greek letter.Includes bibliographical references (p. 57-59).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology