Nielsen type numbers and homotopy minimal periods for maps on the 3-nilmanifolds  

作　　者：Jong Bum LEE 

机构地区：[1]Department of Mathematics,Sogang University, Seoul 121-742, Korea

出　　处：《Science China Mathematics》2008年第3期351-360,共10页中国科学：数学（英文版）

基　　金：the Sogang University (KOREA) Research Grant in 2006 and in part by a grant from ABRL by Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (Grant No. H00021);a BMEC grant (Grant No. KZ200710025012)

摘　　要：For all continuous maps on the 3-nilmanifolds, we give explicit formulae for a complete computation of the Nielsen type numbers NP_n(f)and Nφ_n(f). The most general cases were explored by Heath and Keppelmann and the complementary part is studied in this paper. While studying the homotopy minimal periods of all maps on the 3-nilmanifolds, we also give a complete description of the homotopy minimal periods for all maps on the 3-nilmanifolds, including a correction to Jezierski and Marzantowicz’s result.For all continuous maps on the 3-nilmanifolds, we give explicit formulae for a complete computation of the Nielsen type numbers NP n (f) and NΦ n (f). The most general cases were explored by Heath and Keppelmann and the complementary part is studied in this paper. While studying the homotopy minimal periods of all maps on the 3-nilmanifolds, we also give a complete description of the homotopy minimal periods for all maps on the 3-nilmanifolds, including a correction to Jezierski and Marzantowicz’s result.

关 键 词：homotopy minimal period Nielsen number Nielsen type number NILMANIFOLD 55M20 57S30 

分 类 号：O186.12[理学—数学]