Minimal algebraic complexes overD4n
| Autor: | Seamus O’Shea, W. H. Mannan |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Pure mathematics
non-simply connected homotopy Cell complex Open problem Homotopy 16E05 Wall's D(2) problem algebraic homotopy Disjoint sets 16E10 Mathematics::Algebraic Topology Cohomology 57M20 55Q20 Mathematics::K-Theory and Homology Bundle cancellation of modules 55P15 Geometry and Topology Algebraic number Mathematics |
| Zdroj: | Algebr. Geom. Topol. 13, no. 6 (2013), 3287-3304 |
| ISSN: | 1472-2739 1472-2747 |
| DOI: | 10.2140/agt.2013.13.3287 |
| Popis: | In 1965 Wall showed that for n > 2, if a finite cell complex is cohomologically n– dimensional (in the sense of having no non-trivial cohomology in dimensions above n with respect to any coefficient bundle), then it is in fact homotopy equivalent to an actual n–dimensional cell complex [18]. Subsequently it was shown by Swan [16] and Stallings [15] that the only cohomologically 1–dimensional finite cell complexes are disjoint unions of wedges of circles. However decades later the case nD 2 remains a major open problem, known as Wall’s D(2)–problem. |
| Databáze: | OpenAIRE |
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