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Mosc. Math. J., 2006, Volume 6, Number 1, Pages 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

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.

DOI: https://doi.org/10.17323/1609-4514-2006-6-1-169-194

Full text: http://www.ams.org/.../abst6-1-2006.html
References: PDF file   HTML file

Bibliographic databases:

MSC: Primary 57Q45; Secondary 57Q35
Received: November 14, 2005
Language:

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
\mathnet{http://mi.mathnet.ru/mmj242}
\crossref{https://doi.org/10.17323/1609-4514-2006-6-1-169-194}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2265954}
\zmath{https://zbmath.org/?q=an:1132.57022}
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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. 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
    2. 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
    3. 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
    4. Dobrinskaya N., Turchin V., “Homology of Non-K-Overlapping Discs”, Homol. Homotopy Appl., 17:2 (2015), 261–290  crossref  mathscinet  zmath  isi  elib  scopus
  • Moscow Mathematical Journal
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