Extensions of Quandles and Cocycle Knot Invariants
نویسندگان
چکیده
منابع مشابه
Extensions of Quandles and Cocycle Knot Invariants
Quandle cocycles are constructed from extensions of quandles. The theory is parallel to that of group cohomology and group extensions. An interpretation of quandle cocycle invariants as obstructions to extending knot colorings is given, and is extended to links component-wise.
متن کاملEXTENSIONS OF QUANDLES AND COCYCLE KNOT INVARIANTS by
Approved: Major Professor: Masahiko Saito, Ph.D. Associate Professor, Department of Mathematics Date Approved:
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 کاملTwisted quandle homology theory and cocycle knot invariants
The quandle homology theory is generalized to the case when the coefficient groups admit the structure of Alexander quandles, by including an action of the infinite cyclic group in the boundary operator. Theories of Alexander extensions of quandles in relation to low dimensional cocycles are developed in parallel to group extension theories for group cocycles. Explicit formulas for cocycles cor...
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 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: Journal of Knot Theory and Its Ramifications
سال: 2003
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216503002718