Fundamental classes not representable by products
Fundamental classes not representable by products
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不能用产品代表的基础类
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
C. Loeh
中科院分区：
文献类型：
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作者：
D. Kotschick;C. Loeh
我们证明了具有适当大的基本群的有理本质流形不允许任何来自正维闭流形的乘积的非零度映射。特别的例子包括所有非正截面曲率为秩1的流形和所有非紧型的不可约局部对称空间。对于某些类的闭流形，比如非正曲流形，或者曲面上的某些曲面丛，我们证明了它们确实允许来自非平凡乘积的非零度映射当且仅当它们与乘积几乎同构。
We prove that rationally essential manifolds with suitably large fundamental groups do not admit any maps of non‐zero degree from products of closed manifolds of positive dimension. Particular examples include all manifolds of non‐positive sectional curvature of rank one and all irreducible locally symmetric spaces of non‐compact type. For closed manifolds from certain classes, say non‐positively curved ones, or certain surface bundles over surfaces, we show that they do admit maps of non‐zero degree from non‐trivial products if and only if they are virtually diffeomorphic to products.