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Aug 14, 2013 at 2:44 comment added David Roberts Thanks, Renato. This is the general flavour of how one starts to compute $cat(M)$ for $M$ a manifold - calculate the cup length, and also find an atlas; this gives the lower and upper bounds on $M$. An analogue of the above proposition for my $n$-fold LS-category would be nice.
Aug 14, 2013 at 2:36 history answered Renato G. Bettiol CC BY-SA 3.0