arXiv subjects

Roberto Ladu

Publications and source records attributed to Roberto Ladu.

5 recordsLinked to original sources

arXiv2026

On smooth structures over $4$-manifolds with fundamental group of even order

We show that any topological, closed, oriented, non-spin $4$-manifold with fundamental group $\mathbb{Z}_{4k}$ and $\min(b_2^+, b_2^-)\geq 15$, has either none or infinitely many distinct smooth structures. Furthermore, we construct infinitely many non-diffeomorphic, irreducible, smooth structures on manifolds with signature zero, $b_2^+$ even and fundamental group $\mathbb{Z}_2\times G$, for any finite group $G$. This extends the results of Baykur-Stipsicz-Szab\'o.

math.GT↗

arXiv2025

On $h$-cobordisms of complexity $2$

We study $5$-dimensional $h$-cobordisms of Morgan-Szab\'o complexity $2$. We compute the monopole Floer homology and the action of the twisting involution of the protocork boundary associated with such $h$-cobordisms, obtaining an obstruction for $h$-cobordisms between exotic pairs to have minimal complexity. We construct the first examples of $h$-cobordisms of non-minimal, in fact, arbitrarily large, complexity between an exotic pair of closed, $1$-connected $4$-manifolds. Further applications include strong corks.

math.GT↗

arXiv2024

Protocorks and monopole Floer homology

We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a theorem on the relative Seiberg-Witten invariants of a protocork before and after twisting and a splitting theorem on the Floer homology of protocork boundaries. As a corollary we improve a theorem by Morgan and Szabó regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover, we generalize the result that only the reduced Floer homology of a cork boundary contributes to the variation of the Seiberg-Witten invariants under a cork twist to more general cut and paste operations where the pieces involved are $1$-connected and homeomorphic relative to the boundary.

math.GT↗

arXiv2023

The Akbulut cork is not universal

We exhibit infinitely many exotic pairs of simply-connected, closed $4$-manifolds not related by any cork of the infinite family $W_n$ constructed by Akbulut and Yasui whose first member is the Akbulut cork. In particular, the Akbulut cork is not universal. Moreover we show that, in the setting of manifolds with boundary, there are no $\partial$-universal corks, i.e. there does not exist a cork which relates any exotic pair of simply-connected $4$-manifolds with boundary.

math.GT↗

arXiv2023

Non-smoothable homeomorphisms of $4$-manifolds with boundary

We construct the first examples of non-smoothable self-homeomorphisms of smooth $4$-manifolds with boundary that fix the boundary and act trivially on homology. As a corollary, we construct self-diffeomorphisms of $4$-manifolds with boundary that fix the boundary and act trivially on homology but cannot be isotoped to any self-diffeomorphism supported in a collar of the boundary and, in particular, are not isotopic to any generalised Dehn twist.

math.GT↗