arXiv subjects

R. İnanç Baykur

Publications and source records attributed to R. İnanç Baykur.

4 recordsLinked to original sources

arXiv2026

Exotic S^2 x S^2 candidates that are just fake

We show that two infinite families of homology $S^2\times S^2$'s presented in \cite{FPS, AP}, originally proposed as exotic candidates, are aspherical. In particular, none of these manifolds is an exotic $S^2\times S^2$. We prove this by reconstructing them from aspherical building blocks, following Edmonds. The same arguments apply to and rule out further candidates for simply connected exotica. We also give counterexamples to the conjecture that Luttinger surgery preserves symplectic asphericity.

math.GT↗

arXiv2026

Small Lefschetz fibrations on the BMY line

We give explicit positive factorizations for a genus-19 Lefschetz fibration over the torus and a family of genus-4 Lefschetz fibrations over a genus-2 surface. All these examples have only three nodes, and their total spaces are symplectic 4-manifolds of general type on the Bogomolov-Miyaoka-Yau line. In the course of deriving the monodromy relation in genus 19, we obtain several interesting identities, including a factorization of a Dehn twist into a product of three order-3 mapping classes. We show that the total space of this fibration is topologically s-cobordant to the Cartwright-Steger surface, and we determine its real quotient up to homeomorphism. The genus-4 family consists of variations of the Bauer-Catanese fibrations and contains 65 isomorphism classes of Lefschetz fibrations on 45 diffeomorphism types of compact complex ball quotients. We describe their topology and that of the real quotients of the three original surfaces. The handle monodromies in our main factorizations are pseudo-Anosov, and we show more generally that for holomorphic genus-4 Lefschetz fibrations on the BMY line, this holds for every choice of handle generators.

math.GT↗

arXiv2026

Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions

We construct infinitely many pairwise non-diffeomorphic irreducible smooth four-manifolds homeomorphic to ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$, each admitting a free, orientation-preserving involution. Their quotients give infinitely many irreducible definite four-manifolds with fundamental group ${\mathbb {Z}}/2 {\mathbb {Z}}$ and $b_2=3$, filling the corresponding gap in the geography of such examples. The construction of infinitely many distinct examples relies on a novel equivariant torus surgery.

math.GT↗

arXiv2026

On nonorientable $4$--manifolds

We present several structural results on closed, nonorientable, smooth $4$--manifolds, extending analogous results and machinery for the orientable case. We prove the existence of simplified broken Lefschetz fibrations and simplified trisections on nonorientable $4$--manifolds, yielding descriptions of them via factorizations in mapping class groups of nonorientable surfaces. With these tools in hand, we classify low genera simplified broken Lefschetz fibrations on nonorientable $4$--manifolds. We also establish that every closed, smooth $4$--manifold is obtained by surgery along a link of tori in a connected sum of copies of $\mathbb{CP}^2$, $S^1 \times S^3$ and $S^1\widetilde{\times} S^3$. Our proofs make use of topological modifications of singularities, handlebody decompositions, and mapping classes of surfaces.

math.GT↗