We derive averaging formulas for the Lefschetz coincidence numbers,the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on infra-solvmanifolds modeled on a connected and simply connected so...We derive averaging formulas for the Lefschetz coincidence numbers,the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on infra-solvmanifolds modeled on a connected and simply connected solvable Lie group of type(R).As an application,we compare our formula for the Nielsen coincidence numbers with a result of Jezierski(1992)for pairs of maps on some infra-solvmanifolds of Sol.For all the pairs of self-maps of a nonorientable infra-solvmanifold of Sol,we determine the sets of all the possible values of the Nielsen coincidence numbers and the Reidemeister coincidence numbers.展开更多
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...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.展开更多
基金supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education(Grant No.NRF-2016R1D1A1B01006971)。
文摘We derive averaging formulas for the Lefschetz coincidence numbers,the Nielsen coincidence numbers and the Reidemeister coincidence numbers of maps on infra-solvmanifolds modeled on a connected and simply connected solvable Lie group of type(R).As an application,we compare our formula for the Nielsen coincidence numbers with a result of Jezierski(1992)for pairs of maps on some infra-solvmanifolds of Sol.For all the pairs of self-maps of a nonorientable infra-solvmanifold of Sol,we determine the sets of all the possible values of the Nielsen coincidence numbers and the Reidemeister coincidence numbers.
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)
文摘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.
