Nielsen type numbers and homotopy minimal periods for maps on 3–solvmanifolds

Lee, Jong Bum; Zhao, Xuezhi

doi:10.2140/agt.2008.8.563

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Nielsen type numbers and homotopy minimal periods for maps on $3$–solvmanifolds

Jong Bum Lee and Xuezhi Zhao

Algebraic & Geometric Topology 8 (2008) 563–580

DOI: 10.2140/agt.2008.8.563

Abstract

For all continuous maps on $3$ –solvmanifolds, we give explicit formulas for a complete computation of the Nielsen type numbers $N P_{n} (f)$ and $N Φ_{n} (f)$ . The most general cases were explored by Heath and Keppelmann [Topology Appl. 76 (1997) 217–247] and the complementary part is studied in this paper. While studying the homotopy minimal periods of all maps on $3$ –solvmanifolds, we give a complete description of the sets of homotopy minimal periods of all such maps, including a correction to Jezierski, Kȩedra and Marzantowicz’s results in [Topology Appl. 144 (2004) 29–49].

Keywords

homotopy minimal period, Nielsen number, Nielsen type number, solvmanifold

Mathematical Subject Classification 2000

Primary: 55M20

Secondary: 57S30

References

Publication

Received: 26 February 2007

Accepted: 27 January 2008

Published: 12 May 2008

Authors

Jong Bum Lee
Department of Mathematics Sogang University Seoul 121–742 KOREA

Xuezhi Zhao
Department of Mathematics Institute of Mathematics and Interdisciplinary Science Capital Normal University Beijing 100037 CHINA

Volume 8, issue 1 (2008)