Wiedersehen metrics and exotic involutions of Euclidean spheres

奇异嵌入曲面与来自实Seiberg-Witten理论的反演

Exotic embedded surfaces and involutions from Real Seiberg-Witten theory

本文扩展了Miyazawa的构造，研究了4流形上的反演及非定向曲面的奇异嵌入，利用实Seiberg-Witten理论检测奇异性质，并证明了相关不变量的基本结果。

Smooth structures on non-orientable four-manifolds and free involutions

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-Stern, Gompf, and Stolz. We add to the number of known constructions and provide new examples of exotic manifolds that are obtained as an application of Gluck twists to the standard smooth structure. Inspection of the smooth structure on the oriented 2-covers yields existence results of orientation-reversing exotic free involutions.

不可约的奇异 ${\mathbb {CP}}^2\\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$ 及其自由对合

Irreducible exotic ${\mathbb {CP}}^2\# 7{\overline {\mathbb {C}} {\mathbb {P}} } ^2$'s with free involutions

构造无穷多个同胚于CP²#7(-CP²)但两两不微分同胚的不可约光滑四流形，每个允许保定向自由对合；其商空间给出无穷多个基本群为Z/2Z、b₂=3的不可约定号四流形，填补地理学空白，方法基于新颖的等变环面手术。

An involution acting nontrivially on Heegard-Floer homology

We show that a certain involution on the well known homology sphere (the boundary of the Mazur manifold) induces a nontrivial homomorphism on its Heegard-Floer homology groups (recently defined by Ozsvath and Szabo). We discuss a possible application of this to constructing exotic smooth structures on 4-manifolds.

Knotting corks

It is known that every exotic smooth structure on a simply connected closed 4-manifold is determined by a codimention zero compact contractible Stein submanifold and an involution on its boundary. Such a pair is called a cork. In this paper, we construct infinitely many knotted imbeddings of corks in 4-manifolds such that they induce infinitely many different exotic smooth structures. We also show that we can imbed an arbitrary finite number of corks disjointly into 4-manifolds, so that the corresponding involutions on the boundary of the contractible 4-manifolds give mutually different exotic…

Involutions on tori with codimension one fixed point set

The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete topological classification, valid in all dimensions, of the locally linear, orientation reversing, involutions on tori with fixed point set of codimension one.