下解流形的扭曲莱夫谢茨数与代数群
Twisted Lefschetz numbers of infra-solvmanifolds and algebraic groups
摘要：
扭曲莱夫谢茨数是普通莱夫谢茨数对值为平坦丛的上同调的推广。作为零流形上自映射的普通莱夫谢茨数的线性化公式的推广，利用代数群的上同调，证明了任何下可解流形上的自映射的扭莱夫谢茨数等于矩阵$A$的行列式${\rm det}(I-A)$.
英文摘要：
Twisted Lefschetz numbers are extensions of the ordinary Lefschetz numbers for cohomologies with values in flat bundles. As a generalization of linearization formula for the ordinary Lefschetz number of a self-map of a nilmanifold, we show that a twisted Lefschetz number of any self-map of any infra-solvmanifold is equal to the determinant ${\rm det}(I-A)$ for some matrix $A$ by using the cohomology of algebraic groups.
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