19 citations · 45 across the 20 of their papers we have counts for
22 papers
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…
Geography of -manifolds with positive scalar curvature
Agnese Mantione, Rafael Torres
We discuss the geography problem of closed oriented 4-manifolds that admit a Riemannian metric of positive scalar curvature, and use it to survey mathematical work employed to addr…
Existence of Riemannian metrics with positive biorthogonal curvature on simply connected 5-manifolds
Boris Stupovski, Rafael Torres
Using recent work of Bettiol, we show that a first-order conformal deformation of Wilking's metric of almost-positive sectional curvature on yields a family of metr…
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…
An equivalence between pseudo-holomorphic embeddings into almost-complex Euclidean space and CR regular embeddings into complex space
Rafael Torres
We show that a pseudo-holomorphic embedding of an almost-complex -manifold into almost-complex -Euclidean space exists if and only if there is a CR regular embedding…
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…
Existence results of totally real immersions and embeddings into
Marko Slapar, Rafael Torres
We prove that the existence of totally real immersions of manifolds is a closed property under cut-and-paste constructions along submanifolds including connected sums. We study the…
An orbit space of a nonlinear involution of with nonnegative sectional curvature
Rafael Torres
We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a…
Some examples of vanishing Yamabe invariant and minimal volume, and collapsing of inequivalent smoothings and PL-structures
Rafael Torres
In this short note, exploits of constructions of -structures coupled with technology developed by Cheeger-Gromov and Paternain-Petean are seen to yield a procedure to…
A note on collapse, entropy, and vanishing of the Yamabe invariant of symplectic 4-manifolds
Pablo Suárez-Serrato, Rafael Torres
We make use of -structures and technology developed by Paternain - Petean to compute minimal entropy, minimal volume, and Yamabe invariant of symplectic 4-manifolds, a…
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…
On entropies, -structures, and scalar curvature of certain involutions
Rafael Torres
In this short note, we analyze geometric properties of orbit spaces of certain involutions in dimensions four, five, and six. We consider constructions of -structures…
On the number of type change loci of a generalized complex structure
Rafael Torres, Jonathan Yazinski
In this note, we describe a procedure to construct generalized complex structures with an arbitrarily large number of type change loci on products of the circle with a connected su…
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-…
Geography of symplectic 4- and 6-manifolds
Rafael Torres, Jonathan Yazinski
The geography of minimal symplectic 4-manifolds with arbitrary fundamental group and symplectic 6-manifolds with abelian fundamental group of small rank, and with arbitrary fundame…
Constructions of generalized complex structures in dimension four
Rafael Torres
Four-manifold theory is employed to study the existence of (twisted) generalized complex structures. It is shown that there exist (twisted) generalized complex structures that have…
On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
Rafael Torres
In this paper, first we consider the existence and non-existence of Einstein metrics on the topological 4-manifolds $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$ (for $k \in {11, 13, 14…
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…