On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere

Dong Heon Choe, Kyungbae Park

Published 2017-04-14Version 1

We show that, if a rational homology 3-sphere $Y$ bounds a positive definite smooth 4-manifold, then there are finitely many negative definite lattices, up to the stable-equivalence, which can be realized as the intersection form of a smooth 4-manifold bounded by $Y$. To this end, we make use of constraints on definite forms bounded by $Y$ induced from Donaldson's diagonalization theorem, and Ozsv\'ath and Szab\'o's Heegaard Floer correction term. We also present some families of Seifert fibered 3-manifolds that bound both positive and negative definite smooth 4-manifolds.