#### Volume 8, issue 1 (2008)

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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
##### Abstract

For all continuous maps on $3$–solvmanifolds, we give explicit formulas for a complete computation of the Nielsen type numbers $N{P}_{n}\left(f\right)$ and $N{\Phi }_{n}\left(f\right)$. 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
Primary: 55M20
Secondary: 57S30