Geodesic
Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 261-276.

Voir la notice de l'article provenant de la source Math-Net.Ru

Homotopy invariants of free cochain complexes are studied. These invariants are applied to the calculation of exact values of the Morse numbers for smooth manifolds of large dimension. 
@article{TM_2006_252_a20,
     author = {V. V. Sharko},
     title = {Numerical {Invariants} of {Cochain} {Complexes} and the {Morse} {Numbers} of {Manifolds}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {261--276},
     publisher = {mathdoc},
     volume = {252},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2006_252_a20/}
}
TY  - JOUR
AU  - V. V. Sharko
TI  - Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2006
SP  - 261
EP  - 276
VL  - 252
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2006_252_a20/
LA  - ru
ID  - TM_2006_252_a20
ER  - 
%0 Journal Article
%A V. V. Sharko
%T Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2006
%P 261-276
%V 252
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2006_252_a20/
%G ru
%F TM_2006_252_a20
V. V. Sharko. Numerical Invariants of Cochain Complexes and the Morse Numbers of Manifolds. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Geometric topology, discrete geometry, and set theory, Tome 252 (2006), pp. 261-276. http://geodesic.mathdoc.fr/item/TM_2006_252_a20/

[1] Andrica D., Functions with a minimal number of critical points, Preprint 95-8, “Babes-Bolyai” Univ., Cluj-Napoca (Romania), 1995 | Zbl

[2] Bogoyavlenskii O.I., “O tochnoi funktsii na mnogoobraziyakh”, Mat. zametki, 8:1 (1970), 77–83 | Zbl

[3] Cockcroft W.H., Swan R.G., “On the homotopy type of certain two-dimensional complexes”, Proc. London Math. Soc., 11 (1961), 193–202 | DOI | MR | Zbl

[4] Damian A., “On the stable Morse number of a closed manifold”, Bull. London Math. Soc., 34 (2002), 420–430 | DOI | MR | Zbl

[5] Forman R., “Witten–Morse theory for cell complexes”, Topology, 37 (1998), 945–979 | DOI | MR | Zbl

[6] Eliashberg Y., Gromov M., “Lagrangian intersections and the stable Morse theory”, Boll. Uni. mat. Ital. B, 11:2 (1997), 289–326 | MR | Zbl

[7] Farber M., “Homological algebra of Novikov–Shubin invariants and Morse inequalities”, Geom. and Funct. Anal., 6 (1996), 628–665 | DOI | MR | Zbl

[8] Gromov M., Shubin M., “Near-cohomology of Hilbert complexes and topology of non-simply connected manifolds”, Astérisque, 210 (1992), 283–294 | MR | Zbl

[9] Hajduk B., “Comparing handle decompositions of homotopy equivalent manifolds”, Fund. math., 95 (1977), 35–47 | MR | Zbl

[10] Kirby R.C., Siebenmann L.C., Foundational essays on topological manifolds, smoothings and triangulations, Ann. Math. Stud., 88, Princeton Univ. Press, Princeton (NJ), 1977 | MR | Zbl

[11] Lück W., $L^2$-invariants: Theory and applications to geometry and $K$-theory, Springer, Berlin, 2002 | MR

[12] Mathai V., Shubin M., “Twisted $L^2$-invariants of non-simply connected manifolds and asymptotic $L^2$ Morse inequalities”, Russ. J. Math. Phys., 4 (1996), 499–526 | MR | Zbl

[13] Novikov S.P., Shubin M.A., “Neravenstva Morsa i algebry fon Neimana”, UMN, 41:4 (1986), 163–164

[14] Novikov S.P., Shubin M.A., “Neravenstva Morsa i neimanovskie $\mathrm{II}_1$-faktory”, DAN SSSR, 289:2 (1986), 289–292 | MR | Zbl

[15] Novikov S.P., Shubin M.A., “Teoriya Morsa i neimanovskie invarianty neodnosvyaznykh mnogoobrazii”, UMN, 41:5 (1986), 222–223

[16] Pajitniov A., “On the asymptotics of Morse numbers of finite covers of manifolds”, Topology, 38 (1999), 529–541 | DOI | MR

[17] Sharko V., “$L^2$-invariants of manifolds and cell complexes”, Topology and Geometry, Proc. Ukr. Math. Congr., 2001, Inst. Math. NAS Ukr., Kyiv, 2003, 103–135 | MR | Zbl

[18] Sharko V.V., Functions on manifolds: Algebraic and topological aspects, Transl. Math. Monogr., 131, Amer. Math. Soc., Providence (RI), 1993 | MR | Zbl

[19] Stallings J., “A finitely presented group whose 3-dimensional integral homology is not finitely generated”, Amer. J. Math., 85 (1963), 541–543 | DOI | MR | Zbl

[20] Witten E., “Supersymmetry and Morse theory”, J. Diff. Geom., 17 (1982), 661–692 | MR | Zbl