We show that the bulk-edge correspondence for two-dimensional type A and type AII topological insulators follows directly from the cobordism invariance of the index.

2018-04-06math-phmath.KTmath.MP

族指数的协方差不变性

Cobordism invariance of the family index

给出了族指数协边不变性的K-理论证明。考虑紧致底空间B上具有光滑纤维的连续纤维丛上的椭圆伪微分族，并利用边界纤维丛上的K^1-群定义了共边族的概念。我们证明了两个这样的族的指数是相同的，利用K-理论中的前推映射的性质将其约化为B x R^n上的族。

2009-11-06math.KT

关于Carvalho的$K$ --指数协边不变性的理论公式

On Carvalho's $K$-theoretic formulation of the cobordism invariance of the index

本文给出了一个解析证明，证明了当主象征来自内部的一个$K$ -理论类的限制时，紧流形边界上的椭圆算子的指数为零.证明使用非交换残基内的尖点伪微分算子的Melrose演算。

2006-12-08math.APmath.KT

指数协方差不变性的K理论证明

A K-Theory Proof of the Cobordism Invariance of the Index

本文证明了σ紧流形上椭圆型伪微分算子的指数的协边不变性，其中在非紧情形下，假设椭圆型伪微分算子是紧集外的乘法算子.我们证明了，如果流形X边界上的椭圆算子的主象征类对K^1（TX）有适当的扩张，则它的指数为零。这个条件被纳入非紧流形的配边群的定义中，这里称为“符号的配边”。我们的证明是拓扑的，因为我们使用了Atiyah和Singer定义的K理论中的前推映射的性质，将其约化为R^n。特别地，我们将指数关于前推映射的不变性推广到非紧情形，并将Atiyah和Singer的K-理论指数公式推广到紧集外的乘法算子.我们的结果也适用于G-等变算子，其中G是一个紧李群。

2004-08-19math.GTmath.KT

Cobordism invariance of topological edge-following states

We prove that a spectral gap-filling phenomenon occurs whenever a Hamiltonian operator encounters a coarse index obstruction upon compression to a domain with boundary. Furthermore, the gap-filling spectra contribute to quantised current channels, which follow and are localised at the possibly complicated boundary. This index obstruction is shown to be insensitive to deformations of the domain boundary, so the phenomenon is generic for magnetic Laplacians modelling quantum Hall systems and Chern topological insulators. A key construction is a quasi-equivariant version of Roe's algebra of local…

2021-10-05cond-mat.mes-hallmath-phmath.KT

代数配边与代数 K-理论的 Conner-Floyd 同构

Algebraic cobordism and a Conner-Floyd isomorphism for algebraic K-theory

本文研究了非A^1不变的动机谱稳定∞范畴，利用P^1和加权A^1同伦不变性定义了万有定向动机环谱MGL，并证明了任意qcqs派生概形的代数K理论可通过Conner-Floyd同构从其MGL上同调中恢复。

2024-02-14math.AGmath.ATmath.KT

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HPD-invariance of the Tate conjecture

We prove that the Tate conjecture is invariant under Homological Projective Duality (=HPD). As an application, we prove the Tate conjecture in the new cases of linear sections of determinantal varieties, and also in the cases of complete intersections of two quadrics. Furthermore, we extend the Tate conjecture from schemes to stacks and prove it for certain global orbifolds

2017-11-30math.AGmath.ATmath.KT

HPD-invariance of the Tate, Beilinson and Parshin conjectures

We prove that the Tate, Beilinson and Parshin conjectures are invariant under Homological Projective Duality (=HPD). As an application, we obtain a proof of these celebrated conjectures (as well as of the strong form of the Tate conjecture) in the new cases of linear sections of determinantal varieties and complete intersections of quadrics. Furthermore, we extend the original conjectures of Tate, Beilinson and Parshin from schemes to stacks and prove these extended conjectures for certain low-dimensional global orbifolds.

2018-05-03math.AGmath.ATmath.KT

非紧超曲面的分区流形指标定理

A partitioned manifold index theorem for noncompact hypersurfaces

该研究将Roe的分区流形指标定理从紧超曲面情形推广到非紧超曲面情形，在嵌入假设下得到N的Roe代数K-理论中两类的等式，补充了相关领域的研究成果。

2025-07-30math.DGmath.KTmath.OA

A KK-theoretic perspective on deformed Dirac operators

We study the index theory of a class of perturbed Dirac operators on non-compact manifolds of the form $\mathsf{D}+\mathrm{i}\mathsf{c}(X)$, where $\mathsf{c}(X)$ is a Clifford multiplication operator by an orbital vector field with respect to the action of a compact Lie group. Our main result is that the index class of such an operator factors as a KK-product of certain KK-theory classes defined by $\mathsf{D}$ and $X$. As a corollary we obtain the excision and cobordism-invariance properties first established by Braverman. An index theorem of Braverman relates the index of $\mathsf{D}+\mathr…

2021-01-14math.DGmath.KT