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Jul 29, 2010 at 13:38 comment added Jeff Strom The L-S category gives a lower bound on the number of critical points of a functional on your manifold. That's the big abstract theorem that Lusternik and Schnirelmann proved.
Oct 26, 2009 at 17:31 comment added j.c. For the L-S category, having an upper bound on the category can bound the complexity of your manifold (e.g. in terms of cohomology) from above
Oct 26, 2009 at 16:15 comment added Sonia Balagopalan Is this appropriate as an answer? I would have commented on the question if I had the rep.
Oct 26, 2009 at 16:05 history answered Sonia Balagopalan CC BY-SA 2.5