Abstract
We develop a version of -theory for an -algebra (i.e., the -theory of pointed G-sets for a pointed monoid G) and establish its first properties. We construct a Cartan assembly map to compare the Chu-Morava -theory for finite pointed groups with our -theory. We compute the -theory groups for finite pointed groups in terms of stable homotopy of some classifying spaces. We introduce certain ...
Abstract
We develop a version of -theory for an -algebra (i.e., the -theory of pointed G-sets for a pointed monoid G) and establish its first properties. We construct a Cartan assembly map to compare the Chu-Morava -theory for finite pointed groups with our -theory. We compute the -theory groups for finite pointed groups in terms of stable homotopy of some classifying spaces. We introduce certain Loday-Whitehead groups over that admit functorial maps into classical Whitehead groups under some reasonable hypotheses. We initiate a conjectural formalism using combinatorial Grayson operations to address the Equivariant Nishida Problem-it asks whether admits operations that endow with a pre--ring structure, where G is a finite group and is the G-fixed point spectrum of the equivariant sphere spectrum.
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