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
Abstract

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].

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