AI 中文总结
研究从拓扑空间\(X\)到\(m\)维流形\(M\)的\(p\)个映射\(f_1,\cdots,f_p\)，定义勒夫谢茨型同态\(\Lambda_{f_1\cdots f_p}\)，通过其非平凡性判定映射是否有公共点，且该同态可表示为类似Knill的迹。
AI 中文摘要
给定从任意拓扑空间\(X\)到可定向闭连通\(m\)维流形\(M\)的\(p\)个映射\(f_1,\cdots,f_p\)（\(p\geq2\)），本文定义了一个度数为\(-m(p - 1)\)的分次同态\(\Lambda_{f_1\cdots f_p}:H(X)\to H(M^{p - 1})\)，称为勒夫谢茨同态。若该同态非平凡，则存在\(x\in X\)使得\(f_1(x)=\cdots=f_p(x)\)，且它可表示为类似Knill的迹。
英文摘要
Given $p$-maps $f_1, \cdots, f_p : X \to M,$ $p \geq 2,$ from an arbitrary topological space to an orientable closed connected $m$-manifold, in this paper we define a graded homomorphism $Λ_{f_1 \cdots f_p}: H(X) \to H(M^{p-1})$ of degree $-m(p-1)$ called by Lefschetz homomorphism. If the Lefschetz homomorphism is nontrivial then there is a point $x \in X$ such that $f_1(x) = \cdots = f_p(x).$ The Lefschetz homomorphism $Λ_{f_1 \cdots f_p}$ can be represented as a Knill-like trace.
