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Obstruction theory for coincidences of multiple maps. (arXiv:1602.06911v2 [math.AT] UPDATED)
来源于:arXiv
Let $f_1,..., f_k:X\to N$ be maps from a complex $X$ to a compact manifold
$N$, $k\ge 2$. In previous works \cite{BLM,MS}, a Lefschetz type theorem was
established so that the non-vanishing of a Lefschetz type coincidence class
$L(f_1,...,f_k)$ implies the existence of a coincidence $x\in X$ such that
$f_1(x)=...=f_k(x)$. In this paper, we investigate the converse of the
Lefschetz coincidence theorem for multiple maps. In particular, we study the
obstruction to deforming the maps $f_1,...,f_k$ to be coincidence free. We
construct an example of two maps $f_1,f_2:M\to T$ from a sympletic $4$-manifold
$M$ to the $2$-torus $T$ such that $f_1$ and $f_2$ cannot be homotopic to
coincidence free maps but for {\it any} $f:M\to T$, the maps $f_1,f_2,f$ are
deformable to be coincidence free. 查看全文>>