Volume 8, issue 1 (2008)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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

For all continuous maps on 3–solvmanifolds, we give explicit formulas for a complete computation of the Nielsen type numbers NPn(f) and NΦn(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].

homotopy minimal period, Nielsen number, Nielsen type number, solvmanifold
Mathematical Subject Classification 2000
Primary: 55M20
Secondary: 57S30
Received: 26 February 2007
Accepted: 27 January 2008
Published: 12 May 2008
Jong Bum Lee
Department of Mathematics
Sogang University
Seoul 121–742
Xuezhi Zhao
Department of Mathematics
Institute of Mathematics and Interdisciplinary Science
Capital Normal University
Beijing 100037