${\mathbb{Z}}_2$-coefficient homology $(1,2)$-systolic freedom of $\mathbb{R}{\mathbb{P}}^3$ # $\mathbb{R}{\mathbb{P}}^3$

Lizhi Chen

We prove the $3$-manifold $\RP^3 \# \RP^3$ is of ${\mathbb{Z}}_2$-coefficient homology $(1,2)$-systolic freedom. Given a Riemannian metric on $\RP^{3}\# \RP^{3}$, we define ${\mathbb{Z}}_2$-coeff…