Banach Algebras and Rational Homotopy Theory
| dc.creator | Lupton, Gregory | |
| dc.creator | Phillips, N. Christopher | |
| dc.creator | Schochet, Claude L. | |
| dc.creator | Smith, Samuel B. | |
| dc.date | 2005-09-12 | |
| dc.date | 2007-04-27 | |
| dc.date.accessioned | 2026-07-07T07:58:25Z | |
| dc.date.available | 2026-07-07T07:58:25Z | |
| dc.description | Let $A$ be a unital commutative Banach algebra with maximal ideal space $X.$ We determine the rational H-type of the group $GL_n (A)$ of invertible n by n matrices with coefficients in A, in terms of the rational cohomology of $X.$ We also address an old problem of J. L. Taylor. Let $Lc_n (A)$ denote the space of "last columns" of $GL_n (A).$ For $n > 1 + s/2,$ we construct a natural isomorphism from the rational Cech cohomology group $H^s (X; Q)$ to the rational homotopy group $π_{2 n - 1 - s} (Lc_n (A)) \otimes Q,$ which shows that the rational cohomology groups of $X$ are determined by a topological invariant associated to $A.$ As part of our analysis, we determine the rational H-type of certain gauge groups $F (X, G)$ for $G$ a Lie group or, more generally, a rational H-space. | |
| dc.description | 29 pages, AMSLaTeX2e, uses xypic. Version 2 contains various minor corrections and improvements (including additional references), and is to appear in Trans. AMS | |
| dc.identifier | https://arxiv.org/abs/math/0509269 | |
| dc.identifier | http://arxiv.org/abs/math/0509269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128000 | |
| dc.subject | Algebraic Topology | |
| dc.subject | Functional Analysis | |
| dc.subject | 46J05, 46L85, 55P62, 54C35, 55P15, 55P45 | |
| dc.title | Banach Algebras and Rational Homotopy Theory | |
| dc.type | text |