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Izv. Akad. Nauk SSSR Ser. Mat., 1971, Volume 35, Issue 4, Pages 831–843 (Mi izv2060)  

This article is cited in 23 scientific papers (total in 23 papers)

On the theory of generalized manifolds

E. G. Sklyarenko

Abstract: A simple construction is given for proving the Poincaré duality theorem for generalized manifolds, which also applies to generalized manifolds without locally constant “orientation” sheaves (for example, to manifolds with “boundary”). It appears that some other well-known duality relations in generalized manifolds are either special cases of Poincaré duality, or simple consequences of it.

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English version:
Mathematics of the USSR-Izvestiya, 1971, 5:4, 845–857

Bibliographic databases:

UDC: 513.83
MSC: 57B10, 55C05, 55B30
Received: 06.07.1970

Citation: E. G. Sklyarenko, “On the theory of generalized manifolds”, Izv. Akad. Nauk SSSR Ser. Mat., 35:4 (1971), 831–843; Math. USSR-Izv., 5:4 (1971), 845–857

Citation in format AMSBIB
\by E.~G.~Sklyarenko
\paper On the theory of generalized manifolds
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1971
\vol 35
\issue 4
\pages 831--843
\jour Math. USSR-Izv.
\yr 1971
\vol 5
\issue 4
\pages 845--857

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    This publication is cited in the following articles:
    1. V. G. Miryuk, “Homology and cohomology of sets and their neighborhoods”, Math. USSR-Sb., 21:2 (1973), 303–315  mathnet  crossref  mathscinet  zmath
    2. A. È. Kharlap, “Local homology and cohomology, homology dimension and generalized manifolds”, Math. USSR-Sb., 25:3 (1975), 323–349  mathnet  crossref  mathscinet  zmath
    3. I. A. Shvedov, “On Aleksandrov's obstruction theorem”, Russian Math. Surveys, 31:5 (1976), 194–197  mathnet  crossref  mathscinet  zmath
    4. A. Yu. Volovikov, “A generalization of the Borsuk–Ulam theorem”, Math. USSR-Sb., 36:2 (1980), 195–202  mathnet  crossref  mathscinet  zmath  isi
    5. E. G. Sklyarenko, “On homology theory associated with the Aleksandrov–Čech cohomology”, Russian Math. Surveys, 34:6 (1979), 103–137  mathnet  crossref  mathscinet  zmath
    6. V. D. Golovin, “On the homology theory of analytic sheaves”, Math. USSR-Izv., 16:2 (1981), 239–260  mathnet  crossref  mathscinet  zmath  isi
    7. E. G. Sklyarenko, “On homologically locally connected spaces”, Math. USSR-Izv., 17:3 (1981), 601–614  mathnet  crossref  mathscinet  zmath  isi
    8. A. Yu. Volovikov, “On the Bourgin–Yang theorem”, Russian Math. Surveys, 35:3 (1980), 196–200  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. Yu. Volovikov, “Mappings of free $\mathbf Z_p$-spaces into manifolds”, Math. USSR-Izv., 20:1 (1983), 35–53  mathnet  crossref  mathscinet  zmath
    10. E. G. Sklyarenko, “Some applications of the functor $\varprojlim^1$”, Math. USSR-Sb., 51:2 (1985), 367–387  mathnet  crossref  mathscinet  zmath
    11. E. G. Sklyarenko, “Connection homology and cohomology between sets. Enclosure homology and cohomology of a closed set”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 307–335  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    12. E. G. Sklyarenko, “On the nature of homological products and duality”, Russian Math. Surveys, 49:1 (1994), 151–215  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. E. G. Sklyarenko, “Hyper(co)homology for exact left covariant functors and a homology theory for topological spaces”, Russian Math. Surveys, 50:3 (1995), 575–611  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. E. G. Sklyarenko, “On homological products”, Izv. Math., 61:1 (1997), 161–181  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. E. G. Sklyarenko, “The Thom isomorphism for nonorientable bundles”, J. Math. Sci., 136:5 (2006), 4166–4200  mathnet  crossref  mathscinet  zmath  elib  elib
    16. E. G. Sklyarenko, “Dual Homology for the de Rham Cohomology”, Proc. Steklov Inst. Math., 247 (2004), 217–226  mathnet  mathscinet  zmath
    17. E. G. Sklyarenko, “On locally free Abelian groups”, Math. Notes, 77:1 (2005), 112–116  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. A. Yu. Volovikov, “Coincidence points of maps of $\mathbb Z_p^n$-spaces”, Izv. Math., 69:5 (2005), 913–962  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. Lisica J., “Strong Bonding Homology and Cohomology”, Topology Appl., 153:2-3 (2005), 394–447  crossref  isi
    20. D. V. Artamonov, “Local Homology and Dimensional Full-Valuedness”, Math. Notes, 81:5 (2007), 573–589  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    21. E. G. Sklyarenko, “Two Orientations”, Math. Notes, 83:1 (2008), 88–96  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    22. E. G. Sklyarenko, “The homological degree and Hopf's absolute degree”, Sb. Math., 199:11 (2008), 1687–1713  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    23. D. V. Artamonov, “On the Lefschetz coincidence theorem”, Sb. Math., 200:7 (2009), 943–979  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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