Surgery Approach to Rudyaks Conjecture

Using the surgery we prove the following: THEOREM. Let $f:M to N$ be a normal map of degree one between closed manifolds with $N$ being $(r-1)$-connected, $rge 1$. If $N$ satisfies the inequality $dim N leq 2r cat N - 3$, then for the Lusternik-Schnirelmann category $cat M geq cat N$ .