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作 者:杨昭[1]
出 处:《数学年刊(A辑)》2011年第2期237-244,共8页Chinese Annals of Mathematics
基 金:国家自然科学基金(No.10931005);上海市自然科学基金(No.10ZR1403600)资助的项目
摘 要:设π:M^n→P^n是P^n上的小覆盖,S是P^n的任意一个n-1维截面.给出了π^(-1)(S)是n-1维闭子流形(或者两个相互同胚n-1维闭子流形的不交并),以及π^(-1)(S)是n-1维伪流形的充要条件.Let π^ : Mn →P^n be a small cover of P^n, S an (n- 1) dimensional section of P^n. The author deals with the relationship between S and π^-1 (S), and obtains a necessary and suKicient condition to guarantee that π-1 (S) is an (n-1) dimensional closed submanifold (or the disjoint union of two (n - 1) dimensional closed submanifolds which are homeomorphic to each other), and a necessary and sufficient condition to guarantee that π-1(S) is an (n - 1)-dimensional pseudomanifold.
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