A K-theoretic refinement of topological realization of unstable algebras
| dc.creator | Yau, Donald | |
| dc.date | 2002-09-04 | |
| dc.date | 2002-11-12 | |
| dc.date.accessioned | 2026-07-07T04:50:35Z | |
| dc.date.available | 2026-07-07T04:50:35Z | |
| dc.description | In this paper we propose and partially carry out a program to use $K$-theory to refine the topological realization problem of unstable algebras over the Steenrod algebra. In particular, we establish a suitable form of algebraic models for $K$-theory of spaces, called $ψ^p$-algebras, which give rise to unstable algebras by taking associated graded algebras mod $p$. The aforementioned problem is then split into (i) the \emph{algebraic} problem of realizing unstable algebras as mod $p$ associated graded of $ψ^p$-algebras and (ii) the \emph{topological} problem of realizing $ψ^p$-algebras as $K$-theory of spaces. Regarding the algebraic problem, a theorem shows that every connected and even unstable algebra can be realized. We tackle the topological problem by obtaining a $K$-theoretic analogue of a theorem of Kuhn and Schwartz on the so-called Realization Conjecture. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0209032 | |
| dc.identifier | http://arxiv.org/abs/math/0209032 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64842 | |
| dc.subject | Algebraic Topology | |
| dc.subject | 55S10, 55S25 | |
| dc.title | A K-theoretic refinement of topological realization of unstable algebras | |
| dc.type | text |