A finite loop space not rationally equivalent to a compact Lie group

Summary, in English

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.

• Författare: Kasper Andersen; Tilman Bauer; Jesper Grodal; Erik Kjær Pedersen
• Publiceringsår: 2004
• Språk: Engelska
• Sidor: 1-10
• Publikation/Tidskrift/Serie: Inventiones Mathematicae
• Volym: 157
• Issue: 1
• Länkar: http://dx.doi.org/10.1007/s00222-003-0341-4
• Dokumenttyp: Artikel i tidskrift
• Förlag: Springer
• Ämne: Mathematics
• Status: Published
• ISBN/ISSN/Övrigt: ISSN: 1432-1297