[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2019.59.3.563

Note on the Codimension Two Splitting Problem

Matsumoto, Yukio (Department of Mathematics, Gakushuin University)

Publication Information

Kyungpook Mathematical Journal / v.59, no.3, 2019 , pp. 563-589 More about this Journal

Abstract

Let W and V be manifolds of dimension m + 2, M a locally flat submanifold of V whose dimension is m. Let $f:W{\rightarrow}V$ be a homotopy equivalence. The problem we study in this paper is the following: When is f homotopic to another homotopy equivalence $g:W{\rightarrow}V$ such that g is transverse regular along M and such that $g{\mid}g^{-1}(M):g^{-1}(M){\rightarrow}M$ is a simple homotopy equivalence? $L{\acute{o}}pez$ de Medrano (1970) called this problem the weak h-regularity problem. We solve this problem applying the codimension two surgery theory developed by the author (1973). We will work in higher dimensions, assuming that $m{\geq_-}5$ .

Keywords

codimension two splitting problem; weak h-regularity problem; codimension two surgery; surgery obstruction; relatively non-singular Hermitian K-theory;

Citations & Related Records

Reference

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