Minimal Euler Characteristics of 4-manifolds with 3-manifold groups

Abstract

Let $\pi ={\pi }_1(M)$ for a compact 3-manifold $M$, and let ${\chi }_4$, $p$ and $q^{\ast }$ be the invariants of Hausmann-Weinberger, Kotschick and Hillman respectively. For certain class of compact 3-manifolds $M$, including all those not containing two-sided $R{P}^2$, we determine ${\chi }_4(\pi )$. We address when does ${\chi }_4(\pi )=p(\pi )$, when does ${\chi }_4(\pi )=q^{\ast }(\pi )$, and answer a question raised by Hillman.

16 pages. This version has been accepted for publication at Science China Mathematics

References in corpus (2)

• Stable classification of 4-manifolds with 3-manifold fundamental groups
• Minimizing Euler characteristics of symplectic four-manifolds