The Arone–Goodwillie spectral sequence for Σ∞Ωnand topological realization at odd primes
| Autor: | Fabian Hebestreit, Manfred Stelzer, Oliver Röndigs, Sebastian Büscher |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Algebraic & Geometric Topology. 13:127-169 |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2013.13.127 |
| Popis: | A basic task of algebraic topology is to construct meaningful algebraic invariants of topological spaces. Singular cohomology can be viewed as such an invariant, but in many different ways. In order to specify the algebraic natures of singular cohomology appearing in this article, fix a finite prime field Fp as coefficients. A rather elementary view is to consider H .X /, the direct sum of all cohomology groups of a topological space X , as a graded Fp –vector space. Via cup product, it in addition becomes an Fp –algebra. Furthermore, H .X / is a module over the Steenrod algebra Ap , the algebra of all stable operations in singular cohomology with Fp –coefficients. The realization question under consideration is whether a given algebraic structure, for example an Ap –module M or an Ap –algebra A, is isomorphic to H .X / for some topological space. There are some obvious restrictions (the module should be unstable), but also more delicate ones. Nick Kuhn formulated the following realization conjecture in [16]. |
| Databáze: | OpenAIRE |
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