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FAKE THREE CONNECTED COVERINGS OF LIE GROUPS
 

Summary: FAKE THREE CONNECTED COVERINGS
OF LIE GROUPS
J. Aguad´e, C. Broto and M. Santos
1. Introduction. In [1] it was proved that for each prime p there are infinitely many fake
3-connected coverings of S3
. By "fake" we mean spaces with the same mod p cohomology
than S3
3 (as algebras over the Steenrod algebra) but different p-completed homotopy
type. After that work was completed one could wonder if the existence of such fake spaces
was a general phenomenon and, in particular, if one could use the same methods to produce
fake three connected coverings of other Lie groups beside S3
. In this paper we prove that
the results of [1] cannot be extrapolated since, indeed, there is homotopy uniqueness up
to p-completion for 3-connected coverings of several compact connected Lie groups and
p-compact groups.
If p is a regular prime for the compact connected Lie group G then S3
is a direct factor
of G at the prime p and one can trivially construct infinitely many fake G 3 out of the
fake S3
3 constructed in [1]. If p is quasi-regular for G in the sense of [10] then G splits

  

Source: Aguadé, Jaume - Departament de Matemàtiques, Universitat Autònoma de Barcelona

 

Collections: Mathematics