Abstract:
For manifolds Mn, n⩾6, with free Abelian fundamental group and four-connected universal covering, the author proves the sharpness of Novikov's inequalities for rational cohomology classes ξ∈H1(M,Q) belonging to an open everywhere dense set U⊂H1(M,R).
Figures: 1.
Bibliography: 20 titles.
Citation:
A. V. Pajitnov, “On the sharpness of Novikov type inequalities for manifolds with free Abelian fundamental group”, Math. USSR-Sb., 68:2 (1991), 351–389
\Bibitem{Paj89}
\by A.~V.~Pajitnov
\paper On the sharpness of Novikov type inequalities for manifolds with free Abelian fundamental group
\jour Math. USSR-Sb.
\yr 1991
\vol 68
\issue 2
\pages 351--389
\mathnet{http://mi.mathnet.ru/eng/sm1672}
\crossref{https://doi.org/10.1070/SM1991v068n02ABEH001933}
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This publication is cited in the following 12 articles:
Stefan Friedl, Laurentiu Maxim, “Twisted Novikov homology of complex hypersurface complements”, Mathematische Nachrichten, 290:4 (2017), 604
Tobias Ekholm, Ivan Smith, “Exact Lagrangian immersions with a single double point”, J. Amer. Math. Soc., 29:1 (2015), 1
Toshitake Kohno, Andrei Pajitnov, “Novikov homology, jump loci and Massey products”, centr.eur.j.math, 12:9 (2014), 1285
M. Farber, D. Schütz, “Closed 1-forms in topology and dynamics”, Russian Math. Surveys, 63:6 (2008), 1079–1139
Dirk Schütz, “On the Whitehead group of Novikov rings associated to irrational homomorphisms”, Journal of Pure and Applied Algebra, 208:2 (2007), 449
F. Reese Harvey, Giulio Minervini, “Morse Novikov theory and cohomology with forward supports”, Math Ann, 335:4 (2006), 787
St. Petersburg Math. J., 18:5 (2007), 809—835
Shubin M., “Semiclassical Asymptotics on Covering Manifolds and Morse Inequalities”, Geom. Funct. Anal., 6:2 (1996), 370–409
LêHông Vân, Kaoru Ono, “Symplectic fixed points, the Calabi invariant and Novikov homology”, Topology, 34:1 (1995), 155
François Latour, “Existence de l-formes fermées non singulières dans une classe de cohomologie de de Rham”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 80:1 (1994), 135
Pazhitnov A., “Morse-Theory of Closed 1-Forms”, Lect. Notes Math., 1474 (1991), 98–110
A. V. Pajitnov, “Modules over some localizations of the ring of Laurent polynomials”, Math. Notes, 46:5 (1989), 856–862
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