Cocycle Invariants and Oriented Singular Knots
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DOI: 10.1007/s00009-021-01867-6
Abstract: We extend the quandle cocycle invariant to oriented singular knots and links using algebraic structures called \emph{oriented singquandles} and assigning weight functions at both regular and singular crossings. This invariant coincides with the classical cocycle… read more here.
Keywords: cocycle invariants; singular knots; invariants oriented; cocycle ... See more keywords
Algebraic hull of maximal measurable cocycles of surface groups into Hermitian Lie groups
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DOI: 10.1007/s10711-020-00587-7
Abstract: Following the work of Burger, Iozzi and Wienhard for representations, in this paper we introduce the notion of maximal measurable cocycles of a surface group. More precisely, let $$\mathbf {G}$$ G be a semisimple algebraic… read more here.
Keywords: algebraic hull; sigma; cocycle; measurable cocycles ... See more keywords
The heptagon-wheel cocycle in the Kontsevich graph complex
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DOI: 10.1080/14029251.2017.1418060
Abstract: The real vector space of non-oriented graphs is known to carry a differential graded Lie algebra structure. Cocycles in the Kontsevich graph complex, expressed using formal sums of graphs on n vertices and 2n −… read more here.
Keywords: kontsevich graph; heptagon wheel; cocycle; graph complex ... See more keywords
Zero Lyapunov exponents and monodromy of the Kontsevich–Zorich cocycle
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DOI: 10.1215/00127094-3715806
Abstract: We describe all the situations in which the Kontsevich-Zorich cocycle has zero Lyapunov exponents. Confirming a conjecture of Forni, Matheus, and Zorich, this only occurs when the cocycle satisfies additional geometric constraints. We also describe… read more here.
Keywords: monodromy kontsevich; zorich cocycle; cocycle; kontsevich zorich ... See more keywords