A Duality Theorem for Reidemeister Torsion

摘要: [a, pf] = f]P, where f ] denotes the value of function at a. If A is free and finitely generated, then clearly A* * can be identified with A. Note that any homomorphism h: A, -* A2 gives rise to a dual h*: -+ A*. As an example consider following geometrical situation. Let M simplical complex whose underlying space oriented n-manifold without boundary. 11 group fixed point simplicial automorphisms M. Then chain Cq(M; Z) considered as left module over integral ring Z[LI]. Now suppose has cell subdivision M'. Cn-q(M'; also Z[fl]-module. We will assume quotient MIR compact, so these modules are generated. There canonical anti-automorphism p Z[lI] which takes each element w into s'l.