Anti-orientation. Lens Space Homeomorphism

In the paper,we shall utilize V.Turaev's sign-refined torsion to investigate the problem of existence of orientation-reversing self-homeomorphism on lens space.V.Turaev has given the sufficient and necessary conditions under dimension three by his sign-refined torsion,we shall focus the orientation-reversing involutions and 4-periodic orientation-reversing self-homeomorphisms on higher-dimensional lens space,we shall present a new proof of a classical result with sign-refined torsion, and use it to study the conditions under which there exits an orientation-reversing involution on the lens space of dimension4l+1.At the last we study 4-periodic orientation-reversing self-homeomorphism on the lens space of dimension 4l + 3 by the techniques of algebraic topology and achieve a necessary condition.