Geodesic
On the abstract \v Cech cohomology
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 41-59.

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

The present Note is a survey of the authors' papers [11, 12, 14, 16–18], concerning the introduction and study of the notion of the abstract Čech cohomology, as well as its applications. Here we have investigated: projective systems, injective systems, covering of a directed partially ordered set, abstract Čech cohomology, abstract Čech homology, Čech cohomology space, simplicial projective systems, de Rham cohomology space of projective systems, J-resolution of a projective system and acyclic resolution. 
@article{BASM_2011_2_a3,
     author = {R. Miron and Gh. Piti\c{s} and I. Pop},
     title = {On the abstract \v {Cech} cohomology},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {41--59},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a3/}
}
TY  - JOUR
AU  - R. Miron
AU  - Gh. Pitiş
AU  - I. Pop
TI  - On the abstract \v Cech cohomology
JO  - Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
PY  - 2011
SP  - 41
EP  - 59
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a3/
LA  - en
ID  - BASM_2011_2_a3
ER  - 
%0 Journal Article
%A R. Miron
%A Gh. Pitiş
%A I. Pop
%T On the abstract \v Cech cohomology
%J Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica
%D 2011
%P 41-59
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a3/
%G en
%F BASM_2011_2_a3
R. Miron; Gh. Pitiş; I. Pop. On the abstract \v Cech cohomology. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2011), pp. 41-59. https://geodesic-test.mathdoc.fr/item/BASM_2011_2_a3/

[1] Cataranciuc S., Soltan P., “Abstract complexes, their homologies and applications”, Bul. Acad. Stiinţe Repub. Moldova. Matematica, 2010, no. 2(63), 31–58 | MR | Zbl

[2] Čech E., “Théorie générale de l'homologie dans un espace quelconque”, Fundam. Math., 19 (1932), 149–183 | Zbl

[3] Costinescu N. C., “Cohomologie à valeurs dans un faisceau cellulaire simple”, Analele Ştiinţifice ale Univ. Al. I. Cuza Iaşi, Seria Noua, Secţiunea I a Mat., 30 (1984), 59–62 | MR | Zbl

[4] Costinescu N. C., Contribuţii în Topologia Algebrică. Şirul spectral Atiyah–Hirzebruch şi $K$-teorie, Thesis, Univ. Bucureşti, 1982

[5] Deheuvels R., “Homologie à coefficients dans un antifaisceau”, C. R. Acad. Sci., 250 (1960), 2492–2494, Paris | MR | Zbl

[6] Deheuvels R., “Homologie des ensembles ordonnés et des espaces topologiques”, Bulletin de la Soc. Math. de France, 90 (1962), 261–321 | MR | Zbl

[7] Dogaru O., “Fascicule celulare simple”, Studii şi Cercetări Matematice, 5:27 (1975), 535–545 | MR

[8] Dogaru O., Teleman K., “Sur une classe de faisceaux”, Rev. Roum. Math. Pures Appl., 28 (1983), 577–581 | MR | Zbl

[9] Godement R., Théorie des faisceaux, Ed. Hermann, Paris, 1958 | MR | Zbl

[10] Godement R., Topologie algèbrique et théorie des faisceaux, Hermann, Paris, 1972 | MR

[11] Miron R., Pop I., “On the abstract Čech homology and cohomology”, Proc. of the Institute of Math., 1974, 57–60, Iaşi | MR

[12] Miron R., Pop I., Topologie Algebrică. Omologie. Spaţii de acoperire, Ed. Acad. RSR, Bucureşti, 1974 | MR | Zbl

[13] Nguyen V. D., “Calculul unor grupuri $K(S^{2n-1}/G)$, II”, Studii şi Cercetări Matematice, 26:6 (1974), 899–928 | MR | Zbl

[14] Pitiş Gh., “Une méthode de calcul des groupes de cohomologie de Čech abstraite”, Memoriile Sectiilor Stiintifice ale Academiei Romane, Series IV, 2 (1979), 87–96

[15] Pitiş Gh., Coomologia structurilor integrabile, Ph. D. Thesis, University Al. I. Cuza, Iaşi, 1981

[16] Pitiş Gh., “$J$-resolutions of a projective system”, Bul. Univ. Braşov, Ser. C, 23 (1981), 85–88 (Romanian) | MR | Zbl

[17] Pitiş Gh., “Suites spectrales and $J$-résolutions d'un système projectif”, An. Ştiinţ. Univ. Al. I. Cuza, Iaşi, N. Ser., Secţ. I a, 30 (1984), 89–94 | MR | Zbl

[18] Pop I., “An application of the abstract Čech cohomology”, Bull. Math. Soc. Sci. Math. Repub. Soc. Roum., Nouv. Sér., 28:76 (1984), 369–374 | MR | Zbl

[19] Soltan P., “On the Homologies of Multy-ary relations and Oriented Hipergraphs”, Studii în metode de analiză numerică şi optimizare, 2:1(3) (2000), 60–81 | MR

[20] Spanier E. H., Algebraic topology, McGraw-Hill Series in Higher Math., McGraw-Hill Book Co, New York etc., 1966 | MR | Zbl

[21] Teleman C., Elemente de topologie şi varietăţi diferenţiabile, Editura Didactică şi Pedagogică, Bucureşti, 1964 | MR | Zbl