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Uspekhi Mat. Nauk, 1988, Volume 43, Issue 4(262), Pages 11–55 (Mi umn1833)  

This article is cited in 38 scientific papers (total in 38 papers)

Homological dimension theory

A. N. Dranishnikov


Full text: PDF file (3032 kB)
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English version:
Russian Mathematical Surveys, 1988, 43:4, 11–63

Bibliographic databases:

UDC: 515.142.221
MSC: 12G10, 57T10, 20K01, 20K30, 20K40
Received: 10.03.1988

Citation: A. N. Dranishnikov, “Homological dimension theory”, Uspekhi Mat. Nauk, 43:4(262) (1988), 11–55; Russian Math. Surveys, 43:4 (1988), 11–63

Citation in format AMSBIB
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\by A.~N.~Dranishnikov
\paper Homological dimension theory
\jour Uspekhi Mat. Nauk
\yr 1988
\vol 43
\issue 4(262)
\pages 11--55
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\transl
\jour Russian Math. Surveys
\yr 1988
\vol 43
\issue 4
\pages 11--63
\crossref{https://doi.org/10.1070/RM1988v043n04ABEH001900}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. R.J. Daverman, “Hereditarily aspherical compacta and cell-like maps”, Topology and its Applications, 41:3 (1991), 247  crossref
    2. S. M. Ageev, “Classifying spaces for free actions, and the Hilbert–Smith conjecture”, Russian Acad. Sci. Sb. Math., 75:1 (1993), 137–144  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Yu. V. Lubenets, “The fundamental dimension of subcompacta”, Russian Math. Surveys, 47:3 (1992), 182–183  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A.N. Dranishnikov, “Stable cohomotopy dimension and weakly infinite dimensional spaces”, Topology and its Applications, 47:1 (1992), 79  crossref
    5. A. N. Dranishnikov, “The Eilenberg–Borsuk theorem for mappings into an arbitrary complex”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 467–475  mathnet  crossref  mathscinet  zmath  isi
    6. Takahisa Miyata, “COHOMOLOGICAL DIMENSION OF UNIFORM SPACES”, Quaestiones Mathematicae, 19:1-2 (1996), 137  crossref
    7. Alexander N. Dranishnikov, Dušan Repovs, “Cohomological dimension with respect to perfect groups”, Topology and its Applications, 74:1-3 (1996), 123  crossref
    8. Jerzy Dydak, “Extension Theory: The interface between set-theoretic and algebraic topology”, Topology and its Applications, 74:1-3 (1996), 225  crossref
    9. A.N. Dranishnikov, J.E. West, “Compact group actions that raise dimension to infinity”, Topology and its Applications, 80:1-2 (1997), 101  crossref
    10. E. V. Shchepin, “Arithmetic of dimension theory”, Russian Math. Surveys, 53:5 (1998), 975–1069  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. L. V. Bogachev, E. B. Yarovaya, “A limit theorem for a supercritical branching random walk on $\mathbb Z^d$ with a single source”, Russian Math. Surveys, 53:5 (1998), 1086–1088  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Bogatyi, SA, “The geometry of maps into Euclidean space”, Russian Mathematical Surveys, 53:5 (1998), 893  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. A.N. Dranishnikov, D. Repovš, E.V. Ščepin, “Transversal intersection formula for compacta”, Topology and its Applications, 85:1-3 (1998), 93  crossref
    14. Katsuya Yokoi, “Localization in dimension theory”, Topology and its Applications, 84:1-3 (1998), 269  crossref
    15. S. M. Ageev, D. Repovš, “Fine homotopy equivalence and injectivity”, Math. Notes, 65:6 (1999), 770–772  mathnet  crossref  crossref  mathscinet  zmath  isi
    16. A.N. Dranishnikov, “Boundaries of Coxeter groups and simplicial complexes with given links”, Journal of Pure and Applied Algebra, 137:2 (1999), 139  crossref
    17. A. N. Dranishnikov, “Asymptotic topology”, Russian Math. Surveys, 55:6 (2000), 1085–1129  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    18. Katsuya Yokoi, “Edwards-Walsh resolutions of complexes and Abelian groups”, BAZ, 62:3 (2000), 407  crossref  mathscinet  zmath  isi
    19. A Dranishnikov, “On Alexandroff theorem for general Abelian groups”, Topology and its Applications, 111:3 (2001), 343  crossref  elib
    20. Jerzy Dydak, Akira Koyama, “Cohomological dimension of locally connected compacta”, Topology and its Applications, 113:1-3 (2001), 39  crossref
    21. Akira Koyama, Katsuya Yokoi, “On Dranishnikov's cell-like resolution”, Topology and its Applications, 113:1-3 (2001), 87  crossref
    22. S. A. Bogatyi, “Topologicheskaya teorema Khelli”, Fundament. i prikl. matem., 8:2 (2002), 365–405  mathnet  mathscinet  zmath
    23. A.N. Dranishnikov, “A generalization of Borsuk's pasting theorem and its application”, Topology and its Applications, 120:1-2 (2002), 169  crossref
    24. Akira Koyama, Katsuya Yokoi, “Cohomological dimension and acyclic resolutions”, Topology and its Applications, 120:1-2 (2002), 175  crossref
    25. V. V. Fedorchuk, “Fully closed mappings and their applications”, J. Math. Sci., 136:5 (2006), 4201–4292  mathnet  crossref  mathscinet  zmath  elib  elib
    26. Dranishnikov, AN, “Large Riemannian manifolds which are flexible”, Annals of Mathematics, 157:3 (2003), 919  crossref  mathscinet  zmath  isi
    27. Dydak, J, “Extension theory of infinite symmetric products”, Fundamenta Mathematicae, 182:1 (2004), 53  crossref  mathscinet  zmath  isi  elib
    28. Rubin, LR, “Resolutions for metrizable compacta in extension theory”, Transactions of the American Mathematical Society, 358:6 (2006), 2507  crossref  mathscinet  zmath  isi
    29. D. V. Artamonov, “Local Homology and Dimensional Full-Valuedness”, Math. Notes, 81:5 (2007), 573–589  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    30. V. V. Fedorchuk, “Weakly infinite-dimensional spaces”, Russian Math. Surveys, 62:2 (2007), 323–374  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    31. A.N. Dranishnikov, “Cohomological dimension of Markov compacta”, Topology and its Applications, 154:7 (2007), 1341  crossref
    32. V. V. Fedorchuk, “Dimension scales of bicompacta”, Siberian Math. J., 49:3 (2008), 549–561  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    33. Tulsi Srinivasan, “On the Lusternik–Schnirelmann category of Peano continua”, Topology and its Applications, 2013  crossref
    34. Alexander Dranishnikov, Michael Levin, “On dimensionally exotic maps”, Isr. J. Math, 2014  crossref
    35. Dranishnikov A., Levin M., “Dimension of the Product and Classical Formulae of Dimension Theory”, Trans. Am. Math. Soc., 366:5 (2014), 2683–2697  isi
    36. Dranishnikov A.N., “Dimension of Compact Metric Spaces”, Indag. Math.-New Ser., 29:1, SI (2018), 429–449  crossref  isi
    37. Levin M., “On the Unstable Intersection Conjecture”, Geom. Topol., 22:5 (2018), 2511–2532  crossref  isi
    38. P. S. Gevorkyan, “Teoriya sheipov”, Fundament. i prikl. matem., 22:6 (2019), 19–84  mathnet
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