论文信息 - An Infinite Family of Non‐Invertible Surfaces in 4‐Space

An Infinite Family of Non‐Invertible Surfaces in 4‐Space

A proof is given that for each non‐negative integer g, there is an infinite family of knotted surfaces of genus g, none of which is ambient isotopic to itself with the orientation reversed. 2000 Mathematics Subject Classification 57Q45, 57R42.

S. Satoh | Soichiro Asami

[1] Jozef H. Przytycki,et al. 3-coloring and other elementary invariants of knots , 2006, math/0608172.

[2] C. Gordon. ON THE REVERSIBILITY OF TWIST-SPUN KNOTS , 2003 .

[3] T. Mochizuki. Some calculations of cohomology groups of finite Alexander quandles , 2003 .

[4] S. Satoh. SURFACE DIAGRAMS OF TWIST-SPUN 2-KNOTS , 2002 .

[5] Roger Fenn,et al. KNOTTED SURFACES AND THEIR DIAGRAMS (Mathematical Surveys and Monographs 55) , 2000 .

[6] M. Saito,et al. SHIFTING HOMOMORPHISMS IN QUANDLE COHOMOLOGY AND SKEINS OF COCYCLE KNOT INVARIANTS , 2000, math/0006175.

[7] C. Rourke,et al. A new classification of links and some calculations using it , 2000, math/0006062.

[8] Masahico Saito,et al. Quandle cohomology and state-sum invariants of knotted curves and surfaces , 1999, math/9903135.

[9] M. Saito,et al. Knotted Surfaces and Their Diagrams , 1997 .

[10] S. Matveev. DISTRIBUTIVE GROUPOIDS IN KNOT THEORY , 1984 .

[11] Daniel Ruberman. DOUBLY SLICE KNOTS AND THE CASSON-GORDON INVARIANTS , 1983 .

[12] R. Fox. Metacyclic Invariants of Knots and Links , 1970, Canadian Journal of Mathematics.

[13] J. Levine,et al. Polynomial Invariants of Knots of Codimension Two , 1966 .

[14] E. Zeeman,et al. Twisting spun knots , 1965 .

[15] David Joyce,et al. A classifying invariant of knots, the knot quandle , 1982 .