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We show that the Waldhausen trace map $mathrm{Tr}_X colon A(X) to QX_+$, which defines a natural splitting map from the algebraic $K$-theory of spaces to stable homotopy, is natural up to emph{weak} homotopy with respect to transfer maps in algebraic $K$-theory and Becker-Gottlieb transfer maps respectively.
For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in the faces. F
For $Gamma$ a relatively hyperbolic group, we construct a model for the universal space among $Gamma$-spaces with isotropy on the family VC of virtually cyclic subgroups of $Gamma$. We provide a recipe for identifying the maximal infinite virtually c
In this note we show that Waldhausens K-theory functor from Waldhausen categories to spaces has a universal property: It is the target of the universal global Euler characteristic, in other words, the additivization of the functor sending a Waldhause
We construct a model of differential K-theory, using the geometrically defined Chern forms, whose cocycles are certain equivalence classes of maps into the Grassmannians and unitary groups. In particular, we produce the circle-integration maps for th
For G a finite group and X a G-space on which a normal subgroup A acts trivially, we show that the G-equivariant K-theory of X decomposes as a direct sum of twisted equivariant K-theories of X parametrized by the orbits of the conjugation action of G