Related papers: An introduction to exotic 4-manifolds

This invited contribution summarizes some of the more important aspects of exotics. We review theoretical expectations for exotic and nonexotic hybrid mesons, and briefly discuss the leading experimental candidate for an exotic, the…

In this article, we give new means of constructing and distinguishing closed exotic four-manifolds. Using Heegaard Floer homology, we define new closed four-manifold invariants that are distinct from the Seiberg--Witten and Bauer--Furuta…

Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability)…

We reprove and strengthen some old difficult theorems of 4-manifolds by the aid of recently discovered modern tools, which involve contact structures on 3-manifolds, compact Stein domains, etc.

A brief introduction to exterior differential systems for graduate students familiar with manifolds and differential forms. For complete files, see https://github.com/Ben-McKay/introduction-to-exterior-differential-systems

Motivated by a construction of Fintushel and Stern, we show that the topological 4--manifold $CP^2#5{\bar CP^2}$ supports infinitely many distinct smooth structures.

While the exotic diffeomorphisms turned out to be very rich, we know much less about the $b^+_2 =2$ case, as parameterized gauge-theoretic invariants are not well defined. In this paper we present a method (that is, comparing the winding…

Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. In the second paper, we calculate the "smoothness structure" part of the path integral in quantum…

Recent advances in differential topology single out four-dimensions as being special, allowing for vast varieties of exotic smoothness (differential) structures, distinguished by their handlebody decompositions, even as the coarser…

We construct an example of a cork that remains exotic after taking a connected sum with $S^2 \times S^2$. Combined with a work of Akbulut-Ruberman, this implies the existence of an exotic pair of contractible 4-manifolds which remains…

We initiate the study of exotic Dehn twists along 3-manifolds $\neq S^3$ inside $4$-manifolds, which produces the first known examples of exotic diffeomorphisms of contractible 4-manifolds, more generally of definite 4-manifolds, and exotic…

We give arguments that exotic smooth structures on compact and noncompact 4-manifolds are essential for some approaches to quantum gravity. We rely on the recently developed model-theoretic approach to exotic smoothness in dimension four.…

We introduce a method to detect exotic surfaces without explicitly using a smooth 4-manifold invariant or an invariant of a 4-manifold-surface pair in the construction. Our main tools are two versions of families (Seiberg-Witten)…

In this paper we construct a minimal symplectic 4-manifold and prove it is homeomorphic but not diffeomorphic to CP^2 # 3(-CP^2)

We discuss corks, and introduce new objects which we call plugs. Though plugs are fundamentally different objects, they also detect exotic smooth structures in 4-manifolds like corks. We discuss relation between corks, plugs and rational…

In this talk I summarize the status of exotic mesons, including both theoretical expectations and experimental candidates. The current experimental candidates are ``spin-parity exotics''; since these are most often considered possible…

In this article we construct a new family of simply connected symplectic 4-manifolds with $b_2^+ =1$ and $c_1^2 =2$ which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a…

We give several criteria on a closed, oriented 3-manifold that will imply that it is the boundary of a (simply connected) 4-manifold that admits infinitely many distinct smooth structures. We also show that any weakly fillable contact…

We introduce the concept of pseudo-trisections of smooth oriented compact 4-manifolds with boundary. The main feature of pseudo-trisections is that they have lower complexity than relative trisections for given 4-manifolds. We prove…

We introduce the $2$-nodal spherical deformation of certain singular fibers of genus $2$ fibrations, and use such deformations to construct various examples of simply connected minimal symplectic $4$-manifolds with small topology. More…