Non-Trivial Realizations of Virtual Link Diagrams
نویسنده
چکیده
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2dimensional surface.) We prove that if a minimal genus representation meets certain criteria then there is a minimal genus representation resulting in a knotted realization. Acknowledgement.The views expressed herein are those of the author and do not purport to reflect the position of the United States Military Academy, the Department of the Army, or the Department of Defense. (Copyright 2005.)
منابع مشابه
Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. We generalize this invariant to virtual link diagrams. This result is used to demonstrate that there are...
متن کاملVirtual Knot Theory
This paper is an introduction to the subject of virtual knot theory, a generalization of classical knot theory that I discovered in 1996 [2]. This paper gives the basic definitions, some fundamental properties and a collection of examples. Subsequent papers will treat specific topics such as classical and quantum link invariants and Vassiliev invariants for virtual knots and links in more detai...
متن کاملFilamentations for Virtual Links
Abstract. In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial (see [2]). A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used to detect non-classical virtual knots. We extend these fi...
متن کاملVirtual knots undetected by 1 and 2 - strand bracket polynomials H . A . Dye MADN - MATH
Kishino's knot is not detected by the fundamental group or the bracket polynomial; these invariants cannot differentiate between Kishino's knot and the unknot. However, we can show that Kishino's knot is not equivalent to unknot by applying either the 3-strand bracket polynomial or the surface bracket polynomial. In this paper, we construct two non-trivial virtual knot diagrams, K D and K m , t...
متن کاملMinimal Surface Representations of Virtual Knots and Links
Equivalence classes of virtual knot diagrams are in a one to one correspondence with knot diagrams (decorated immersions of S1) in orientable, closed surfaces modulo stable handle equivalence and Reidemeister moves. Each virtual knot diagram corresponds to a diagram in a unique minimal surface. If a virtual knot diagram is equivalent to a classical knot diagram then this minimal surface is a sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2005