Numerical Invariants of Surfaces in 4-Space
Fujitsugu Hosokawa, Toru Maeda, Shinichi Suzuki · Institutional Repositories DataBase (IRDB) · 1979
This is a continuation of Hosokawa-Kawauchi [4],where they have proposed a concept of unknotted surfaces in the Euclidean 4-space R 4 .In this paper we will introduce two numerical invariants of a surface in 4-space related to it and discuss primary topics of them.Throughout the paper, spaces and maps will be considered in the piecewise-linear category, and we will use the same definitions and notation as [4] unless otherwise stated. Compositions of surfacesBy a surfaee we mean a closed, connected and orientable 2-manifold.For a surface F, g(F) stands for the genus of F. We consider an embedded surface in the oriented 4-space.R 4 or 4-sphere that F is oriented and ZoeaUy flat in R 4 11 S. We will always assume 4 or S.Two surfaces F and F' in R 4 (or s 4 ) are said to be of the same knot type, iff there exists an orientation preserving homeomorphism 1jJ of R 4 (or s 4 ) onto itself such that ljl(F) = F' and ljlj F is also orientation preserving.We denote the knot type of F in R 4 (or s 4 ) by [F], so F