Cobordisms of embeddings of oriented five-dimensional manifolds in Euclidean space

Abstract

515.164The groups Ef~5,k of cobordism classes of embeddings of oriented five-dimensional manifolds in 5 + k-dimensional Euclidean space are studied. It is proved that E~s,3 '~ Z2 and Ef~s, The classes of cobordant embeddings constitute an Abelian group with respect to the disjoint union (defined in an appropriate way). This group is denoted by E~2n,k.In the present paper we study the groups Ef/5,k. We compute the two remaining groups Eft5,3 and Ef~5,a and present their specific generators. More precisely, we describe two embeddings #5,3: S 1 x CP 2 ~ R s and #s,4: SI"xCP 2 ~ R 9 and prove the following theorems. Theorems A and B follow from Proposition 2.1 and the next result.