6 problems

Let $BK$ be the symplectic four-manifold constructed in the paper, and let $V_n$ be the sequence of exotic four-manifolds obtained from $BK$, with $V_1=BK$. For a smooth four-manif…

Let $AP$ be the four-manifold constructed in the paper, and let $Z_n$ be the infinite family of exotic four-manifolds obtained by replacing the final Luttinger surgery with torus s…

Let $AP$ be the four-manifold constructed in the paper, and let $H_2(AP;\mathbb Z)$ denote its second homology group. An embedded surface in $AP$ is homologically essential if its…

Let $M=\Sigma_h\times\Sigma_i$, where $\Sigma_h$ and $\Sigma_i$ are closed, orientable surfaces of genus greater than $1$, and let $A\in H_2(M,\mathbb Z)$. Let $g_m(A)$ denote the…

Let $A\in H_2(\mathbb CP^2,\mathbb Z)$, and let $\Sigma$ be an embedded surface representing $A$. The genus of $\Sigma$ is compared among all embedded surfaces representing the sam…

Let $X=S^2_\lambda\times S^2_1$ have symplectic form … and let $\beta=[S^2\times\{\bullet\}]\in H_2(X,\mathbb Z/2\mathbb Z)$. Write $\eta(X,\omega,\beta)$ for the minimal non-orien…