Cohomological dimension, self-linking, and systolic geometry

摘要: Given a closed manifold M, we prove the upper bound of $${1 \over 2}(\dim M + {\rm{cd}}({{\rm{\pi }}_1}M))$$ for number systolic factors in curvature-free lower total volume spirit M. Gromov’s inequalities. Here “cd” is cohomological dimension. We apply this to show that, case 4-manifold, Lusternik-Schnirelmann category an category. Furthermore, inequality on with b 1(M) = 2 presence nontrivial self-linking class typical fiber its Abel-Jacobi map 2-torus.