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Mat. Sb., 1992, Volume 183, Number 12, Pages 103–116 (Mi msb1098)  

This article is cited in 4 scientific papers (total in 4 papers)

On Zeeman's filtration in homology

E. G. Sklyarenko


Abstract: For a finite complex $K$, Zeeman constructed a spectral sequence, converging to the homology of the complex, of the form $E_2^{pq}=H^q(K;\mathcal H_p)\Rightarrow H_{p-q}(K)$. Special attention was given to the corresponding filtration in the homology of $K$, essentially dependent on the cohomology:
\begin{gather*} H_r(K)=F^0H_r(K)\supset F^1H_r(K)\supset…\supset F^qH_r(K)\supset …,
E_\infty^{pq}=F^qH_r(K)/F^{q+1}H_r(K),\qquad r=p-q, \end{gather*}
where $\mathcal H_p$ is the coefficient system determined by the local homology groups $H_p^x=H_p(K, K\setminus x)$.
The object of the present paper is to show that the Zeeman filtration, although defined in terms of the simplicial structure of the complex, is, in the end, of a general-categorical nature. Due to this fact, a more complete description of its connection with the topology of the space and with the product is obtained.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1994, 77:2, 477–488

Bibliographic databases:

UDC: 515.142.21
MSC: Primary 55N25, 55N30; Secondary 18G35, 18G40, 55M05
Received: 31.01.1992

Citation: E. G. Sklyarenko, “On Zeeman's filtration in homology”, Mat. Sb., 183:12 (1992), 103–116; Russian Acad. Sci. Sb. Math., 77:2 (1994), 477–488

Citation in format AMSBIB
\Bibitem{Skl92}
\by E.~G.~Sklyarenko
\paper On Zeeman's filtration in homology
\jour Mat. Sb.
\yr 1992
\vol 183
\issue 12
\pages 103--116
\mathnet{http://mi.mathnet.ru/msb1098}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1213365}
\zmath{https://zbmath.org/?q=an:0810.55009}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1994SbMat..77..477S}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1994
\vol 77
\issue 2
\pages 477--488
\crossref{https://doi.org/10.1070/SM1994v077n02ABEH003451}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994NF83500013}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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
    2. E. G. Sklyarenko, “On homological products”, Izv. Math., 61:1 (1997), 161–181  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. E. G. Sklyarenko, “Filtrations in hyperhomology”, Math. Notes, 61:4 (1997), 480–483  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Lisica J., “Strong Bonding Homology and Cohomology”, Topology Appl., 153:2-3 (2005), 394–447  crossref  mathscinet  zmath  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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