Quandle cocycles from invariant theory
نویسندگان
چکیده
منابع مشابه
Dehn Twists and Invariant Cocycles
A degeneration of compact Kähler manifolds gives rise to a monodromy action on Betti moduli space H (X,G) = Hom(π1(X), G)/G over smooth fibres with a complex algebraic structure group G being either abelian or reductive. Assume that the singularities of the central fibre is of normal crossing. When G = C, the invariant cocycles arise from the global cocycles. This is no longer true in general. ...
متن کاملCocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the case when there is a group action on the coefficients. First, quandle modules are used to generalize Burau representations and Alexander modules for classical knots. Second, 2-cocycles valued in non-abelian groups are us...
متن کاملQuandle Homology Theory and Cocycle Knot Invariants
This paper is a survey of several papers in quandle homology theory and cocycle knot invariants that have been published recently. Here we describe cocycle knot invariants that are defined in a state-sum form, quandle homology, and methods of constructing non-trivial cohomology classes. 1 Prologue We start with an example and its history. Figure 1 is an illustration of the knotted surface diagr...
متن کاملQuandle-like Structures From Groups
We give a general procedure to construct a certain class of ”quandle-like” structures from an arbitrary group. These structures, which we refer to as pseudoquandles, possess two of the three defining properties of quandles. We classify all pseudoquandles obtained from an arbitrary finitely generated abelian group. We also define the notion of the kernel of an element of a pseudoquandle and prov...
متن کاملA Theory of Algebraic Cocycles
We introduce the notion of an algebraic cocycle as the algebraic analogue of a map to an Eilenberg-MacLane space. Using these cocycles we develop a “cohomology theory” for complex algebraic varieties. The theory is bigraded, functorial, and admits Gysin maps. It carries a natural cup product and a pairing to L-homology. Chern classes of algebraic bundles are defined in the theory. There is a na...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2013
ISSN: 0001-8708
DOI: 10.1016/j.aim.2013.05.022