论文标题
软木塞，互动和Heegaard Floer同源
Corks, involutions, and Heegaard Floer homology
论文作者
论文摘要
在由Hendricks，Manolescu和Zemke开发的代数框架的基础上，我们介绍并研究了一组旨在检测软木塞的浮动理论不变性。我们的不变剂阻碍了给定的相差超过任何同源球，而不是特定的合同歧管。与以前的方法不同，我们没有使用任何封闭的4个manifold拓扑或接触拓扑。取而代之的是，我们适应了来自涉及Heegaard浮动同源性的当地等效性的形式主义。 As an application, we define a modification $Θ^τ_{\mathbb{Z}}$ of the homology cobordism group which takes into account an involution on each homology sphere, and prove that this admits a $\mathbb{Z}^\infty$-subgroup of strongly non-extendable corks.组$θ^τ_{\ mathbb {z}} $也可以看作是对差异型的边界组的完善。使用我们的不变式，我们还建立了几个新的软木塞家族，并证明各种已知的例子是不可扩展的。我们的主要计算工具是一种单调性定理，它限制了在模棱两可的负定定义下的不变性的行为，并且是通过模棱两可的手术来构建此类协同的明确方法。
Building on the algebraic framework developed by Hendricks, Manolescu, and Zemke, we introduce and study a set of Floer-theoretic invariants aimed at detecting corks. Our invariants obstruct the extension of a given involution over any homology ball, rather than a particular contractible manifold. Unlike previous approaches, we do not utilize any closed 4-manifold topology or contact topology. Instead, we adapt the formalism of local equivalence coming from involutive Heegaard Floer homology. As an application, we define a modification $Θ^τ_{\mathbb{Z}}$ of the homology cobordism group which takes into account an involution on each homology sphere, and prove that this admits a $\mathbb{Z}^\infty$-subgroup of strongly non-extendable corks. The group $Θ^τ_{\mathbb{Z}}$ can also be viewed as a refinement of the bordism group of diffeomorphisms. Using our invariants, we furthermore establish several new families of corks and prove that various known examples are strongly non-extendable. Our main computational tool is a monotonicity theorem which constrains the behavior of our invariants under equivariant negative-definite cobordisms, and an explicit method of constructing such cobordisms via equivariant surgery.
