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Moscow Mathematical Journal, 2006, Volume 6, Number 1, Pages 169–194
DOI: https://doi.org/10.17323/1609-4514-2006-6-1-169-194 (Mi mmj242) 		 
This article is cited in 4 scientific papers (total in 4 papers)

What is one-term relation for higher homology of long knots

V. É. Turchinab

a Independent University of Moscow
b Université catholique de Louvain
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DOI: https://doi.org/10.17323/1609-4514-2006-6-1-169-194
Abstract: Vassiliev's spectral sequence for long knots is discussed. Briefly speaking we study what happens if the strata of non-immersions are ignored.
Various algebraic structures on the spectral sequence are introduced. General theorems about these structures imply, for example, that the bialgebra of chord diagrams is polynomial for any field of coefficients.
Key words and phrases: Knot spaces, discriminant, bialgebra of chord diagrams, sphere, Hopf algebra with divided powers, simplicial algebra.
Received: November 14, 2005
Bibliographic databases:
MSC: Primary 57Q45; Secondary 57Q35
Language: English
Citation: V. É. Turchin, “What is one-term relation for higher homology of long knots”, Mosc. Math. J., 6:1 (2006), 169–194
Citation in format AMSBIB
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\by V.~\'E.~Turchin
\paper What is one-term relation for higher homology of long knots
\jour Mosc. Math.~J.
\yr 2006
\vol 6
\issue 1
\pages 169--194
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2265954}
\zmath{https://zbmath.org/?q=an:1132.57022}
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  • https://www.mathnet.ru/eng/mmj/v6/i1/p169
    • This publication is cited in the following 4 articles:
    1. Dobrinskaya N., Turchin V., “Homology of Non-K-Overlapping Discs”, Homol. Homotopy Appl., 17:2 (2015), 261–290  crossref  mathscinet  zmath  isi  elib  scopus
    2. Lambrechts P., Turchin V., Volić I., “The rational homology of spaces of long knots in codimension >2”, Geom. Topol., 14:4 (2010), 2151–2187  crossref  mathscinet  zmath  isi
    3. Lambrechts P., Turchin V., “Homotopy graph-complex for configuration and knot spaces”, Trans. Amer. Math. Soc., 361:1 (2009), 207–222  crossref  mathscinet  zmath  isi  elib  scopus
    4. Tourtchine V., “On the other side of the bialgebra of chord diagrams”, J. Knot Theory Ramifications, 16:5 (2007), 575–629  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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