scholarly journals Concordance of Seifert surfaces

2019 ◽  
Vol 298 (2) ◽  
pp. 429-444
Author(s):  
Robert Myers
Keyword(s):  
Seifert Surfaces

Finding Disjoint Seifert Surfaces

1988 ◽  
Vol 20 (1) ◽  
pp. 61-64 ◽  
Author(s):  
Martin Scharlemann ◽  
Abigail Thompson
Keyword(s):  
Seifert Surfaces

scholarly journals SEIFERT SURFACES, COMMUTATORS AND VASSILIEV INVARIANTS

2007 ◽  
Vol 16 (10) ◽  
pp. 1295-1329
Author(s):  
E. KALFAGIANNI ◽  
XIAO-SONG LIN
Keyword(s):  
Fundamental Group ◽  
Lower Central Series ◽  
Central Series ◽  
Seifert Surface ◽  
Vassiliev Invariants ◽  
Seifert Surfaces

We show that the Vassiliev invariants of a knot K, are obstructions to finding a regular Seifert surface, S, whose complement looks "simple" (e.g. like the complement of a disc) to the lower central series of its fundamental group. We also conjecture a characterization of knots whose invariants of all orders vanish in terms of their Seifert surfaces.

scholarly journals Quantum Computing, Seifert Surfaces, and Singular Fibers

2019 ◽  
Vol 1 (1) ◽  
pp. 12-22 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Complete Information ◽  
Singular Fiber ◽  
Dynkin Diagrams ◽  
Singular Fibers ◽  
Seifert Surfaces ◽  
Trefoil Knot ◽  
Universal Quantum

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

scholarly journals Totally knotted Seifert surfaces with accidental peripherals

2003 ◽  
Vol 131 (12) ◽  
pp. 3945-3954 ◽  
Author(s):  
Makoto Ozawa ◽  
Yukihiro Tsutsumi
Keyword(s):  
Seifert Surfaces

SEIFERT SURFACES IN KNOT COMPLEMENTS

2007 ◽  
Vol 16 (08) ◽  
pp. 1053-1066 ◽  
Author(s):  
ENSIL KANG
Keyword(s):  
Compact Surface ◽  
Seifert Surface ◽  
Normal Surface ◽  
Incompressible Surface ◽  
Ideal Triangulation ◽  
Seifert Surfaces ◽  
Knot Complements

In the ordinary normal surface for a compact 3-manifold, any incompressible, ∂-incompressible, compact surface can be moved by an isotopy to a normal surface [9]. But in a non-compact 3-manifold with an ideal triangulation, the existence of a normal surface representing an incompressible surface cannot be guaranteed. The figure-8 knot complement is presented in a counterexample in [12]. In this paper, we show the existence of normal Seifert surface under some restriction for a given ideal triangulation of the knot complement.

Sign in / Sign up

Export Citation Format

Share Document