A homotopical viewpoint at the Poisson bracket invariants for tuples of sets

Abstract

We suggest a homotopical description of the Poisson bracket invariants for tuples of closed sets in symplectic manifolds. It implies that these invariants depend only on the union of the sets along with topological data. 1 Introduction 995 2 ε-pseudoretracts 1000 3 The invariants Pb n 1003 4 The invariant Pb X (α) 1017 References 1026We define invariants, Pb N , of N -tuples of cyclically intersecting compact subsets of a symplectic manifold M . For a compact M they can be defined