Intersectional pairs of $n$-knots, local moves of $n$-knots, and their associated invariants of $n$-knots
Abstract
Let $n$ be an integer$\geqq0$. Let $S^{n+2}_1$ (respectively, $S^{n+2}_2$) be the $(n+2)$-sphere embedded in the $(n+4)$-sphere $S^{n+4}$. Let $S^{n+2}_1$ and $S^{n+2}_2$ intersect transversely. Suppose that the smooth submanifold, $S^{n+2}_1 \cap S^{n+2}_2$ in $S^{n+2}_i$ is PL homeomophic to the $n$-sphere. Then $S^{n+2}_1$ and $S^{n+2}_2$ in $S^{n+2}_i$ is an $n$-knot $K_i$. We say that the pair $(K_1,K_2)$ of n-knots is realizable. We consider the following problem in this paper. Let $A_1$ and $A_2$ be n-knots. Is the pair $(A_1,A_2)$ of $n$-knots realizable? We give a complete characterization.
- Publication:
-
arXiv e-prints
- Pub Date:
- March 2018
- DOI:
- 10.48550/arXiv.1803.03496
- arXiv:
- arXiv:1803.03496
- Bibcode:
- 2018arXiv180303496O
- Keywords:
-
- Mathematics - Geometric Topology
- E-Print:
- 22 pages, 1 figure,Chapter I: Mathematical Research Letters, 1998, 5, 577-582. Chapter II: University of Tokyo preprint series UTMS 95-50. This paper is beased on the author's master thesis 1994, and his PhD thesis 1996