One-parameter Lefschetz class of homotopies on torus

Abstract

The main result this paper states that if $F:T\times I\to T$ is a homotopy on torus then the one-parameter Lefschetz class $L(F)$ of $F$ is given by $L(F)=\pm N(F)\alpha$, where $N(F)$ is the one-parameter Nielsen number of $F$ and $\alpha$ is one of the two generators in $H_1({\pi }_1(T),\mathbb{Z})$.

arXiv commentarXiv admin note: text overlap with arXiv:1309.0669