Algebra i Analiz
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Algebra i Analiz:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Algebra i Analiz, 2006, Volume 18, Issue 5, Pages 173–209 (Mi aa93)  

This article is cited in 12 scientific papers (total in 12 papers)

Research Papers

Novikov homology, twisted Alexander polynomials, and Thurston cones

A. V. Pajitnov

Laboratoire Mathématiques Jean Leray, Université de Nantes, Faculté des Sciences, Nantes
References:
Abstract: 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.
Received: 22.02.2006
English version:
St. Petersburg Mathematical Journal, 2007, Volume 18, Issue 5, Pages 809–CCCXXXV
DOI: https://doi.org/10.1090/S1061-0022-07-00975-2
Bibliographic databases:
Document Type: Article
MSC: 57Rxx
Language: English
Citation: A. V. Pajitnov, “Novikov homology, twisted Alexander polynomials, and Thurston cones”, Algebra i Analiz, 18:5 (2006), 173–209; St. Petersburg Math. J., 18:5 (2007), 809–CCCXXXV
Citation in format AMSBIB
\Bibitem{Paj06}
\by A.~V.~Pajitnov
\paper Novikov homology, twisted Alexander polynomials, and Thurston cones
\jour Algebra i Analiz
\yr 2006
\vol 18
\issue 5
\pages 173--209
\mathnet{http://mi.mathnet.ru/aa93}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2301045}
\zmath{https://zbmath.org/?q=an:1137.57017}
\elib{https://elibrary.ru/item.asp?id=9295936}
\transl
\jour St. Petersburg Math. J.
\yr 2007
\vol 18
\issue 5
\pages 809--CCCXXXV
\crossref{https://doi.org/10.1090/S1061-0022-07-00975-2}
Linking options:
  • https://www.mathnet.ru/eng/aa93
  • https://www.mathnet.ru/eng/aa/v18/i5/p173
  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и анализ St. Petersburg Mathematical Journal
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024