Polyhedron Cross-section And Small Cover Closed Submanifold

LetÏ€:Mnâ†'Pn be a small cover of Pn,S is an(n-1)-dimensional sec-tion of Pn.In this paper we study the relationship between S andÏ€-1(S).We give a necessary and sufficient condition thatÏ€-1(S)is an(n-1)-dimensional closed submanifold(or two(n-1)-dimensional closed submanifolds which are homeomorphic to each other),and a necessary and sufficient condition thatÏ€-1(S)is an(n-1)-dimensional pseudomanifold.