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A finite loop space not rationally equivalent to a compact Lie group | | Kasper K. S. Andersen
; Tilman Bauer
; Jesper Grodal
; Erik K. Pedersen
; | | Date: |
16 Jun 2003 | | Journal: | Invent. Math 157 (2004), no. 1, 1--10. DOI: 10.1007/s00222-003-0341-4 | | Subject: | Algebraic Topology; Geometric Topology MSC-class: 55P35; 55P15, 55R35 | math.AT math.GT | | Abstract: | We construct a connected finite loop space of rank 66 and dimension 1254 whose rational cohomology is not isomorphic as a graded vector space to the rational cohomology of any compact Lie group, hence providing a counterexample to a classical conjecture. Aided by machine calculation we verify that our counterexample is minimal, i.e., that any finite loop space of rank less than 66 is in fact rationally equivalent to a compact Lie group, extending the classical known bound of 5. | | Source: | arXiv, math.AT/0306234 | | Services: | Forum | Review | PDF | Favorites | |
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