Imbedding punctured lens spaces and connected sums

Daniel Ruberman

Vol. 113 (1984), No. 2, 481–491

DOI: 10.2140/pjm.1984.113.481

Abstract

We investigate codimension-one imbeddings of punctured lens spaces and connected sums of lens spaces. For |π₁(L)| a prime power we show that L − B^2k−1 imbeds in S^2k if and only if L is of a certain special form. If L#L′ imbeds in S^2k, then L ≃ L′ and L is homology cobordant to L′. For |π₁(L)| a prime power, this implies (via Smith-theory) that L≅L′.

Mathematical Subject Classification 2000

Primary: 57R40

Milestones

Received: 6 September 1982

Published: 1 August 1984