Triple Point Numbers and Quandle Cocycle Invariants of Knotted Surfaces in 4–space
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چکیده
The triple point number of a knotted surface in 4–space is the minimal number of triple points for all generic projections into 3–space. We give lower bounds of triple point numbers by using cocycle invariants of knotted surfaces. As an application, we give an infinite family of surface–knots of triple point number six. We also study the triple point numbers restricted to generic projections without branch points.
منابع مشابه
Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules
Quandle cohomology theory was developed [5] to define invariants of classical knots and knotted surfaces in state-sum form, called quandle cocycle (knot) invariants. The quandle cohomology theory is a modification of rack cohomology theory which was defined in [11]. The cocycle knot invariants are analogous in their definitions to the Dijkgraaf-Witten invariants [8] of triangulated 3-manifolds ...
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تاریخ انتشار 2014