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Эта публикация цитируется в 12 научных статьях (всего в 12 статьях)
Статьи
Novikov homology, twisted Alexander polynomials, and Thurston cones
A. V. Pajitnov Laboratoire Mathématiques Jean Leray, Université de Nantes, Faculté des Sciences, Nantes
Аннотация:
Let $M$ be a connected CW complex, and let $G$ denote the fundamental group of $M$. Let $\pi$ be an epimorphism of $G$ onto a free finitely generated Abelian group $H$, let $\xi\colon H\to\mathbf R$ be a homomorphism, and let $\rho$ be an antihomomorphism of $G$ to the group $\operatorname{GL}(V)$ of automorphisms of a free finitely generated $R$-module $V$ (where $R$ is a commutative factorial ring).
To these data, we associate the twisted Novikov homology of $M$, which is a module over the Novikov completion of the ring $\Lambda=R[H]$. The twisted Novikov homology provides the lower bounds for the number of zeros of any Morse form whose cohomology class equals $\xi\circ\pi$. This generalizes a result by H. Goda and the author.
In the case when $M$ is a compact connected 3-manifold with zero Euler characteristic, we obtain a criterion for the vanishing of the twisted Novikov homology of $M$ in terms of the corresponding twisted Alexander polynomial of the group $G$.
We discuss the relationship of the twisted Novikov homology with the Thurston norm on the 1-cohomology of $M$.
The electronic preprint of this work (2004) is available from the ArXiv.
Поступила в редакцию: 22.02.2006
Образец цитирования:
A. V. Pajitnov, “Novikov homology, twisted Alexander polynomials, and Thurston cones”, Алгебра и анализ, 18:5 (2006), 173–209; St. Petersburg Math. J., 18:5 (2007), 809–CCCXXXV
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa93 https://www.mathnet.ru/rus/aa/v18/i5/p173
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