Cut and paste invariants of manifolds via algebraic K-theory

余边切割与粘贴群的K-理论谱

A K-theory spectrum for cobordism cut and paste groups

本文构造了一个谱，其在$\pi_0$上恢复带边流形的余边切割粘贴群$\overline{\mathrm{SK}}^{\partial}_n$，并给出提升典范商映射的谱映射。

一个真正的 $G$-谱用于 $G$-流形的剪切-拼接 $K$-理论

A genuine $G$-spectrum for the cut-and-paste $K$-theory of $G$-manifolds

本文证明了等变 $SK$-流形的平方 $K$-理论作为真正 $G$-谱的固定点的猜想，通过构建谱 Mackey 函数来研究剪切-拼接 $K$-理论。

Relating Cut and Paste Invariants and TQFTs

In this paper, we shall be concerned with a relation between TQFTs and cut and paste invariants introduced by Karras, Kreck, Neumann and Ossa. Cut and paste invariants, or SK invariants, are functions on the set of smooth manifolds that are invariant under the cutting and pasting operation. Central to the work in this paper are also SKK invariants, whose values on cut and paste equivalent manifolds differ by an error term depending only on the glueing diffeomorphism. Here we investigate a surprisingly natural group homomorphism between the group of invertible TQFTs and the group of SKK invaria…

实现Tutte多项式作为剪切粘贴K-理论不变量

Realizing the Tutte polynomial as a cut-and-paste K-theoretic invariant

本文利用剪切粘贴K-理论，将Brylawski的Tutte多项式映射实现为K-理论谱映射诱导的K_0-同态，拓展了该工具在拟阵研究中的应用。

Bott-Taubes-Vassiliev cohomology classes by cut-and-paste topology

Bott and Taubes used integrals over configuration spaces to produce finite-type a.k.a. Vassiliev knot invariants. Cattaneo, Cotta-Ramusino and Longoni then used these methods together with graph cohomology to construct "Vassiliev classes" in the real cohomology of spaces of knots in higher-dimensional Euclidean spaces, as first promised by Kontsevich. Here we construct integer-valued cohomology classes in spaces of knots and links in Euclidean spaces of dimension greater than three. We construct such a class for any integer-valued graph cocycle, by the method of gluing compactified configurati…

The Milnor triple-linking number of string links by cut-and-paste topology

Bott and Taubes constructed knot invariants by integrating differential forms along the fiber of a bundle over the space of knots, generalizing the Gauss linking integral. Their techniques were later used to construct real cohomology classes in spaces of knots and links in higher-dimensional Euclidean spaces. In previous work, we constructed cohomology classes in knot spaces with arbitrary coefficients by integrating via a Pontrjagin--Thom construction. We carry out a similar construction over the space of string links, but with a refinement in which configuration spaces are glued together acc…