In more detail, the classical Lusternik-Schnirelmann category catLS(M) of a closed 4-manifold M is an integer between 1 and 4. The systolic category catsys(M) of M was defined in 2006 by M. Katz and Y. Rudyak. The equality of the two categories has been verified both for 2-dimensional complexes and for 3-manifolds, whether orientable or not. Simply connected 4-manifolds satisfy the equality catsys = catLS, as well.
In the hallowed tradition of P. Erdös, we are hereby offering a prize of $50 for an example showing a strict inequality between the two categories for an orientable closed 4-manifold. For European contestants only, the prize is upped to €50. Weigh also other prizes.
See the recent
monograph for further discussion.
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