相关论文: Small Exotic 4-manifolds with b_2^+=3

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…

We consider simply-connected $4$-manifolds admitting Lefschetz fibrations over the $2$-sphere. We explicitly construct nonhyperelliptic and hyperelliptic Lefschetz fibrations of genus $4$ on simply-connected $4$-manifolds which are exotic…

Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic…

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…

It is known that the only Stein filling of the standard contact structure on S^3 is B^4. In this paper, we construct simply connected exotic compact Stein 4-manifold pairs for any Betti number $b_2 \geq 1$; we do this by enlarging corks and…

We construct examples of simply connected nonalgebraic symplectic fourfolds with a prescribed number of nonintersecting symplectic curves with positive self-intersections.

We give new rational blowdown constructions of exotic CP^2#n(-CP^2) (5\leq n\leq 9) without using elliptic fibrations. We also show that our 4-manifolds admit handle decompositions without 1- and 3-handles, for 7\leq n\leq 9. A strategy for…

We construct well-formed and quasismooth terminal Fano 4-folds of index 1 in low codimension containing at worst isolated orbifold points. We provide a certain classification of these varieties where their images under the anitcanonical…

We provide a closed, simply connected, symplectic $6$-manifold having infinitely many codimension $2$ symplectic submanifolds. These are mutually homologous but homotopy inequivalent, and furthermore, they cannot admit complex structures.…

For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group…

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 studied.

We classify topological $4$-manifolds with boundary and fundamental group $\mathbb{Z}$, under some assumptions on the boundary. We apply this to classify surfaces in simply-connected $4$-manifolds with $S^3$ boundary, where the fundamental…

In an article from 2008, A. Akhmedov and B. D. Park constructed irreducible symplectic 4-manifolds homeomorphic but not diffeomorphic to the manifolds CP^2#3CP^2bar and 3CP^2#5CP^2bar. These manifolds are constructed by using generalized…

We show how to construct absolutely exotic smooth structures on compact 4-manifolds with boundary, including contractible manifolds. In particular, we prove that any compact smooth 4-manifold W with boundary that admits a relatively exotic…

It is the purpose of this paper to construct families of examples of nonsymplectic 4-manifolds which (up to sign) have just one Seiberg-Witten basic class.

We construct four infinite families of chiral $3$-polytopes of type $\{4, 8\}$, with $1024m^4$, $2048m^4$, $4096m^4$ and $8192m^4$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are…

We construct infinite families of non-simply connected locally conformally flat (LCF) 4-manifolds realizing rich topological types. These manifolds have strictly negative scalar curvature and the underlying topological 4-manifolds do not…

By gluing some copies of a polytope of Kerckhoff and Storm's, we build the smallest known orientable hyperbolic 4-manifold that is not commensurable with the ideal 24-cell or the ideal rectified simplex. It is cusped and arithemtic, and has…

Closed oriented 4-manifolds with the same geometrically 2-dimensional fundamental group (satisfying certain properties) are classified up to $s$-cobordism by their $w_2$-type, equivariant intersection form and the Kirby-Siebenmann…

We define family versions of the invariant of 4-manifolds with contact boundary due to Kronheimer and Mrowka and use these to detect exotic diffeomorphisms of 4-manifolds with boundary. Further, we show the existence of the first example of…