Author

Anar Akhmedov

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Preprint Oct 2026

A monodromy relation for the Cartwright-Steger fibration

We study the genus-$19$ Albanese fibration of the Cartwright--Steger surface and its order-three symmetry. Passing to the orbifold quotient of the elliptic base gives a relation among the two handle monodromies and the three Dehn twists about the vanishing cycles. The two real vanishing paths give cycles whose real fix...

Anar Akhmedov, Sai-Kee Yeung · 0 citations

Preprint Sep 2026

Braided Surfaces and Small Exotic 4-Manifolds

Let $K$ be the trefoil or figure-eight knot and let $M_K$ denote zero surgery on $K$. We prove that the fiberwise elliptic involution gives a two-fold branched cover \[ M_K\times S^1\longrightarrow T^2\times S^2 \] whose branch locus is a section together with a connected braided three-section. The corresponding braid...

Anar Akhmedov · 0 citations

Preprint Sep 2026

$\mathbb{Z}$-Torus Exteriors and Small Knot-Surgery Four-Manifolds

We study a cut-and-paste operation in which torus neighborhoods in the author's symplectic building blocks $Y_K$ and $X_K$, associated to a genus-one fibered knot $K$, are replaced by marked exteriors of tori in $S^4$ with infinite cyclic complement group and two null peripheral slopes. We also recall the exact Lutting...

Anar Akhmedov · 1 citation · ⚡1

Preprint Sep 2026

Braided Multisections and Symplectic Four-Manifolds with the Rational Cohomology of $S^2\times S^2$

We construct symplectic four-manifolds by taking mixed fiber sums along explicit cyclic multisections in ruled surfaces. For a connected unbranched degree-$p$ multisection in $\Sigma_g\times S^2$, we determine the first homology and fundamental group of the complement and prove that its boundary is incompressible. It f...

Anar Akhmedov · 0 citations