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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 3, Pages 607–643 (Mi izv1257)  

This article is cited in 16 scientific papers (total in 16 papers)

Euler structures, nonsingular vector fields, and torsions of Reidemeister type

V. G. Turaev


Abstract: Combinatorial analogues of nonsingular vector fields on manifolds, so-called Euler structures, are introduced and studied. A refinement of Reidemeister's construction of torsion is proposed that gives new invariants of nonsingular vector fields and Euler structures.
Bibliography: 12 titles.

Full text: PDF file (4455 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 34:3, 627–662

Bibliographic databases:

UDC: 513.836
MSC: Primary 57Q10; Secondary 57R15, 57R25
Received: 19.05.1987

Citation: V. G. Turaev, “Euler structures, nonsingular vector fields, and torsions of Reidemeister type”, Izv. Akad. Nauk SSSR Ser. Mat., 53:3 (1989), 607–643; Math. USSR-Izv., 34:3 (1990), 627–662

Citation in format AMSBIB
\Bibitem{Tur89}
\by V.~G.~Turaev
\paper Euler structures, nonsingular vector fields, and torsions of Reidemeister type
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 3
\pages 607--643
\mathnet{http://mi.mathnet.ru/izv1257}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1013714}
\zmath{https://zbmath.org/?q=an:0692.57015}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 34
\issue 3
\pages 627--662
\crossref{https://doi.org/10.1070/IM1990v034n03ABEH000676}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. SILVIA BENVENUTI, “Hopf ALGEBRAS AND INVARIANTS OF COMBED AND FRAMED 3–MANIFOLDS”, J. Knot Theory Ramifications, 09:02 (2000), 147  crossref
    2. SILVIA BENVENUTI, “Hopf ALGEBRAS AND INVARIANTS OF COMBED AND FRAMED 3–MANIFOLDS”, J. Knot Theory Ramifications, 10:02 (2001), 213  crossref
    3. RICCARDO BENEDETTI, CARLO PETRONIO, “COMBED 3-MANIFOLDS WITH CONCAVE BOUNDARY, FRAMED LINKS, AND PSEUDO-LEGENDRIAN LINKS”, J. Knot Theory Ramifications, 10:01 (2001), 1  crossref
    4. Michael Hutchings, “Reidemeister torsion in generalized Morse theory”, form, 14:2 (2002), 209  crossref  mathscinet  zmath
    5. Maxim Braverman, Thomas Kappeler, “A refinement of the Ray–Singer torsion”, Comptes Rendus Mathematique, 341:8 (2005), 497  crossref
    6. Maxim Braverman, Thomas Kappeler, “Ray–Singer type theorem for the refined analytic torsion”, Journal of Functional Analysis, 243:1 (2007), 232  crossref
    7. Dan Burghelea, Stefan Haller, “Complex-valued Ray–Singer torsion”, Journal of Functional Analysis, 248:1 (2007), 27  crossref
    8. Yuya Koda, “A Heegaard-type presentation of branched spines and the Reidemeister–Turaev torsion”, Math Z, 260:1 (2008), 203  crossref  mathscinet  zmath  isi
    9. Guangxiang Su, Weiping Zhang, “A Cheeger-Müller theorem for symmetric bilinear torsions”, Chin Ann Math Ser B, 29:4 (2008), 385  crossref  mathscinet  zmath  isi
    10. Sylvain E. Cappell, Edward Y. Miller, “Complex-valued analytic torsion for flat bundles and for holomorphic bundles with (1,1) connections”, Comm Pure Appl Math, 2009, NA  crossref
    11. GWÉNAËL MASSUYEAU, “SOME FINITENESS PROPERTIES FOR THE REIDEMEISTER–TURAEV TORSION OF THREE-MANIFOLDS”, J. Knot Theory Ramifications, 19:03 (2010), 405  crossref
    12. Rung-Tzung Huang, Yoonweon Lee, “The gluing formula of the refined analytic torsion for an acyclic Hermitian connection”, manuscripta math, 2011  crossref
    13. Rung-Tzung Huang, Yoonweon Lee, “The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary”, Journal of Geometry and Physics, 2013  crossref
    14. Stefano Borghini, “A gluing formula for Reidemeister–Turaev torsion”, Annali di Matematica, 2014  crossref
    15. GuangXiang Su, “A Cheeger-Müller theorem for symmetric bilinear torsions on manifolds with boundary”, Sci. China Math, 2014  crossref
    16. Osmar Maldonado Molina, “Co-Euler structures on bordisms”, Topology and its Applications, 193 (2015), 51  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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