On lens spaces bounding smooth 4-manifolds with ${\mathbf{b}}_2=1$

Abstract

We study which lens spaces can bound smooth 4-manifolds with second Betti number one under various topological conditions. Specifically, we show that there are infinite families of lens spaces that bound compact, simply-connected, smooth 4-manifolds with second Betti number one, yet cannot bound a 4-manifold consisting of a single 0-handle and 2-handle. Additionally, we establish the existence of infinite families of lens spaces that bound compact, smooth 4-manifolds with first Betti number zero and second Betti number one, but cannot bound simply-connected 4-manifolds with second Betti number one. The construction of such 4-manifolds with lens space boundaries is motivated by the study of rational homology projective planes with cyclic quotient singularities.

21 pages, 15 figures; Added comments and a discussion on Ballinger's related results; comments are welcome

References in corpus (1)

• A simply connected surface of general type with p_g=0 and K^2=2