Mahanta, Snigdhayan (2017) G-theory of F-1-algebras I: the equivariant Nishida problem. JOURNAL OF HOMOTOPY AND RELATED STRUCTURES, 12 (4). pp. 901-930. ISSN 2193-8407, 1512-2891
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ALGEBRAIC K-THEORY; TOPOLOGICAL CYCLIC HOMOLOGY; STABLE-HOMOTOPY GROUPS; SYMMETRIC SPECTRA; ZETA-FUNCTIONS; LOOP SPACE; REPRESENTATIONS; NILPOTENCY; OPERATIONS; F-1; K-theory; G-theory; Monoids; lambda-rings; F-1-algebras; Stable homotopy groups; Equivariant sphere spectrum; Assembly maps; Whitehead groups |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 14 Dec 2018 13:19 |
| Last Modified: | 19 Feb 2019 07:48 |
| URI: | https://pred.uni-regensburg.de/id/eprint/1803 |
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