activity
20062026
most citedExotic smooth structures on 4-manifolds with zero signature

41 citations · 143 across the 25 of their papers we have counts for

collaborators

37 papers

math.AG2026

Xiao's Degree-Four Fibration and the Polizzi Model

Anar Akhmedov, Sümeyra Sakallı

Let be the surface in Xiao's degree-four family identified by Polizzi as a smooth divisor in . Starting from Polizzi's branch model and Xiao's classification of the thi…

math.GT2026

The Real Albanese Map and Smooth Topology of the Cartwright--Steger Quotient

Anar Akhmedov, Sai-Kee Yeung

Let be the Cartwright--Steger surface with its real involution and Albanese map , and put . Every smooth real Albanese fiber has two ovals a…

math.GT2026

A monodromy relation for the Cartwright-Steger fibration

Anar Akhmedov, Sai-Kee Yeung

We study the genus- Albanese fibration of the Cartwright--Steger surface and its order-three symmetry. Passing to the orbifold quotient of the elliptic base gives a relation am…

math.GT2026

Braided Surfaces and Small Exotic 4-Manifolds

Anar Akhmedov

Let be the trefoil or figure-eight knot and let denote zero surgery on . We prove that the fiberwise elliptic involution gives a two-fold branched cover \[ M_K\times S…

math.GT2026

Higher Braided Mixed Sums, Intersection Lattices, and Symplectic Four-Manifolds

Anar Akhmedov, Azer Akhmedov

We study mixed symplectic sums along connected unbranched cyclic multisections of degrees in ruled surfaces. With \[ p(g-1)=q(h-1)=n, \] the resulting four-manifold has…

math.GT2026

Nonabelian Torus Exteriors in and Torus Replacement in Four-Manifolds

Anar Akhmedov, Azer Akhmedov

We study torus-exterior replacement in four-manifolds, with the construction controlled by the peripheral homomorphism. Using torus exteriors arising from the work of Boyle and Kan…