Degrees of self-maps of products
Degrees of self-maps of products
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产品自映射度
DOI：
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发表时间：
2015
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通讯作者：
C. Neofytidis
中科院分区：
文献类型：
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作者：
C. Neofytidis
每个封闭定向流形$M$与整数集$D(M)$相关联，D(M)$是$M$的自映射度集。本文研究当d (M)$和d (N)$都不包含$d$时，积$M\ * N$是否存在阶$d$的自映射。我们找到了D(M\ * N)$恰好包含D(M)$的元素与D(N)$的元素之积的充分条件。因此，我们得到了不允许阶$-1$（强手性）的自映射的流形$M\ * N$，它具有有限的自映射阶集（不灵活），并且不允许素数$p$的阶$dp$的自映射$。进一步，我们得到了奇维强手性双曲流形在其积的自映射度方面的一个表征。
Every closed oriented manifold $M$ is associated with a set of integers $D(M)$, the set of self-mapping degrees of $M$. In this paper we investigate whether a product $M\times N$ admits a self-map of degree $d$, when neither $D(M)$ nor $D(N)$ contains $d$. We find sufficient conditions so that $D(M\times N)$ contains exactly the products of the elements of $D(M)$ with the elements of $D(N)$. As a consequence, we obtain manifolds $M\times N$ that do not admit self-maps of degree $-1$ (strongly chiral), that have finite sets of self-mapping degrees (inflexible) and that do not admit any self-map of degree $dp$ for a prime number $p$. Furthermore we obtain a characterization of odd-dimensional strongly chiral hyperbolic manifolds in terms of self-mapping degrees of their products.