19 citations · 45 across the 20 of their papers we have counts for
10 papers · 1 filter
A novel construction of homotopy 4-spheres and real projective 4-spaces à la Cappell-Shaneson
Rafael Torres
We produce new collections of homotopy 4-spheres and homotopy real projective 4-spaces by extending a classical construction due to Cappell-Shaneson. We use the extension to devise…
Smooth structures on non-orientable -manifolds via twisting operations
Valentina Bais, Rafael Torres
Four observations compose the main results of this note. The first records the existence of a smoothly embedded 2-sphere inside such that performing…
A recipe for exotic 2-links in closed 4-manifolds whose components are topological unknots
Valentina Bais, Younes Benyahia, Oliviero Malech +1
We describe a construction procedure of infinite sets of -links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise t…
Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group
Rafael Torres
We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complemen…
Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
Rafael Torres
We point out that recent constructions of inequivalent smooth structures yield a manufacturing procedure of infinite sets of pairwise smoothly non-isotopic nullhomologous 2-tori an…
Topology change and selection rules for high-dimensional $\Spin(1, n)_0$-Lorentzian cobordisms
Gleb Smirnov, Rafael Torres
We study necessary and sufficient conditions for the existence of Lorentzian and weak Lorentzian cobordisms between closed smooth manifolds of arbitrary dimension such that the str…
Cauchy surfaces and diffeomorphism types of globally hyperbolic spacetimes
Rafael Torres
Chernov-Nemirovski observed that the existence of a globally hyperbolic Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the underlying 4-manifold. In this…
Smooth structures on non-orientable four-manifolds and free involutions
Rafael Torres
In this paper, we investigate existence of inequivalent smooth structures on closed smooth non-orientable 4-manifolds building upon results of Akbulut, Cappell-Shaneson, Fintushel-…
On the geography and botany of irreducible nonspin 4-manifolds with abelian fundamental group
Rafael Torres
The geography and botany of smooth/symplectic nonspin 4-manifolds with abelian fundamental group are addressed.
Irreducible 4-manifolds with abelian non-cyclic fundamental group of small rank
Rafael Torres
A myriad of irreducible symplectic 4-manifolds with abelian non-cyclic fundamental group is constructed. The botany of manifolds with finite non-cyclic fundamental groups is also s…