S. K. Roushon
We study the Fibered Isomorphism Conjecture of Farrell and Jones in L-theory for groups acting on trees. In several cases we prove the conjecture. This includes wreath products of abelian groups and free metabelian groups. We also deduce the conjecture in pseudoisotopy theory for these groups. Finally in B of Theorem 1.1 we prove the L-theory version of [[7], Theorem 1.2].
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We prove the Farrell-Jones fibered isomorphism conjecture for several classes of Artin groups of finite and affine types. As a consequence, we compute explicitly the surgery obstruction groups of the finite type pure Artin groups.
The isomorphism conjecture in L-theory
这是第一个三篇文章的纤维同构猜想法雷尔和琼斯的L-理论。我们将[15]和[16]中发展的一般技巧应用于猜想的L-理论情形，并证明了几个结果。在这里，我们证明了猜想后，倒置2，多自由群。特别地，它适用于辫群。我们还证明了猜想的一些类的群不倒2。事实上，我们考虑满足某些条件的一般类群，其中包括上述群和其他一些重要类群。我们检查我们在[15]中定义的性质在猜想的几个实例中得到满足。
We prove the $K$ and $L$ theoretic versions of the Fibered Isomorphism Conjecture of F. T. Farrell and L. E. Jones for braid groups on a surface.
We study the Fibered Isomorphism conjecture of Farrell and Jones for groups acting on trees. We show that under certain conditions the conjecture is true for groups acting on trees when the stabilizers satisfy the conjecture. These conditions are satisfied in several cases of the conjecture. We prove some general results on the conjecture for the pseudoisotopy theory for groups acting on trees with residually finite vertex stabilizers. In particular, we study situations when the stabilizers belong to the following classes of groups: polycyclic groups, finitely generated nilpotent groups, close…
In this article we study a coarse version of the K-theoretic Farrell-Jones conjecture we call coarse or bounded isomorphism conjecture. With techniques that have already been used to prove the Farrell-Jones conjecture for hyperbolic groups we are able to verify the bounded isomorphism conjecture for spaces of graphs with large girth and bounded geometry.
A Controlled Approach to the Isomorphism Conjecture
我们使用一个hocolim方法的同构猜想在K-理论分析的情况下，组的形式$G\rtimes Z$和$G_1*_{G}G_2$。作为一个重要的推论，我们证明了K-理论中的同构猜想对一个非生成的自由群成立。
We prove the A-theoretic Isomorphism Conjecture with coefficients and finite wreath products for solvable groups.
In this article we study a coarse version of the $K$-theoretic Farrell--Jones conjecture we call coarse or bounded isomorphism conjecture. Using controlled category theory we are able to translate this conjecture for asymptotically faithful covers into a more familiar form. This allows us to prove the conjecture for box spaces of residually finite groups whose Farrell--Jones assembly map with coefficients is an isomorphism.
On the Isomorphism Conjecture in algebraic K-theory
同构猜想是计算群环RG的代数K理论的一种概念性方法，其中G是无限群。本文证明了对于具有严格负截面曲率和任意系数环R的闭黎曼流形基本群，在n<2维中的猜想。如果R是正则的，这就导致了RG的低维K-理论群在R的K-理论和群的同调方面的具体计算。
Given a group, we construct a fundamental additive functor on its orbit category. We prove that any isomorphism conjecture valid for this fundamental isomorphism functor holds for all additive functors, like K-theory, cyclic homology, topological Hochschild homology, etc. Finally, we reduce this fundamental isomorphism conjecture for K-theoretic ones.
In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.
The $KH$-Isomorphism Conjecture and Algebraic $KK$-theory
本文证明了Bartels和L{ü}ck定义的$KH$ -Ask映射可以用Cortinas和Thom的代数$KK$ -理论来描述. $KH$ -装配图的$KK$ -理论描述与Baum-Connes装配图的描述相似。在非常基本的情况下，用于证明鲍姆-康纳斯猜想的方法也适用于$KH$ -同构猜想。
A certain structure of Artin groups and the isomorphism conjecture
本文发现一大类 Artin 群的归纳结构，并据此推导出有限实、复和仿射类型 Artin 群的 Farrell-Jones 同构猜想。
We construct a Dirac morphism and prove that if this Dirac morphism is invertible, then the isomorphism conjecture for non-connective algebraic K-theory holds true.
Inheritance of Isomorphism Conjectures under colimits
我们调查时同构猜想，如由于鲍姆-康纳斯，博斯特和法雷尔-琼斯，是稳定下的colimits的群体在有向集（不一定是内射结构映射）。我们特别表明，无论是K理论的法雷尔-琼斯猜想和博斯特猜想的系数举行的那些群体，希格森，Lafforgue和Skandalis反驳鲍姆-康纳斯猜想的系数。
L^2-Betti numbers, isomorphism conjectures and noncommutative localization
本文讨论了L^2-贝蒂数的合理性问题如何与代数K理论中的同构猜想相联系，以及为什么在这种情况下非交换局部化成为一个重要的工具。
Isomorphism Conjecture for homotopy K-theory and groups acting on trees
本文讨论同伦代数K理论的Farrell-Jones猜想。特别地，我们证明了，如果一个群G作用在一棵树上，并且所有的各向同性群满足这个猜想，那么G满足这个猜想。这个结果可以用来得到代数K理论中Farrell-Jones猜想中集合映射的有理内射性结果。
In this article we study the K- and L-theory of groups acting on trees. We consider the problem in the context of the fibered isomorphism conjecture of Farrell and Jones. We show that in the class of residually finite groups it is enough to prove the conjecture for finitely presented groups with one end. Also, we deduce that the conjecture is true for the fundamental groups of graphs of finite groups and of trees of virtually cyclic groups. To motivate the reader we include a survey on some classical works on this subject.
We show that for various natural classes of groups and appropriately defined K- and L-theoretic functors, injectivity or bijectivity of the assembly map follows from the Isomorphism Conjecture being true for acyclic groups lying within that class.
Algebraic kk-theory and the KH-isomorphism conjecture
本研究借助同伦理论与伴随定理，建立带Weibel同伦K-理论系数的Davis-Lück同调与等变代数kk-理论的联系，并用等变代数kk-群刻画KH同构猜想装配映射的左侧，推进相关代数K-理论猜想研究。
We relate two conjectures which have been raised for classification of Leavitt path algebras. For purely infinite simple unital Leavitt path algebras, it is conjectured that K_0 classifies them completely. For arbitrary Leavitt path algebras, it is conjectured that K^{\gr}_0 classifies them completely \cite{hazann}. We show that for two finite graphs with no sinks (which their associated Leavitt path algebras include the purely infinite simple ones) if their K^{\gr}_0-groups of their Leavitt path algebras are isomorphic then their K_0-groups are isomorphic as well.
Induction Theorems and Isomorphism Conjectures for K- and L-Theory
Farrell-Jones猜想和Baum-Connes猜想认为，对于群G的虚循环子群或有限子群，可以用这些函子计算群环的代数K-理论和L-理论，以及群G的约化群C^*-代数的拓扑K理论。通过归纳理论，我们希望将这些子群族减少到一个更小的族，例如减少到有限超补子群族或具有无限循环核的有限超补群的扩展，或者减少到有限循环子群族。粗略地说，我们把Dress关于有限群的归纳定理推广到了无限群.
Based on results by S.K. Roushon (math.KT/0408243 and math.KT/0405211) this thesis summarizes in an axiomatic way when a Meta-Isomorphism-Conjecture in the sense of Lueck and Reich (math.KT/0402405) is true for fundamental groups of 3-dimensional manifolds. In particular we prove that the fibered Farrell-Jones isomorphism conjectures for L-theory and algebraic K-theory are true for this class of groups if they are true for semidirect products of $\mathbb{Z^2}$ with $\mathbb{Z}$.
Singular equivalences of $n$-adjoint type and standard eventually homological isomorphisms
本文修改最终同调同构定义，引入n-伴随型奇异等价，发展相关理论并应用于同调猜想简化与性质保持，同时建立其与三角函子的对应关系，纳入3-伴随型奇异等价框架。
In this paper we complete the proof of Caldararu's conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects. Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet (the existence of the latter was conjectured by Tsygan). We also rely on the fact - recently proved by the first two authors - t…
A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold
Tsygan关于链的形式结构的证明将开启重要的代数工具，这可能导致Atiyah-Patodi-Singer指标定理和Riemann-Roch-Hirzebruch定理的新推广。尽管这一关键作用，在传统的调查和各种人的努力，最普遍的版本Tsygan的形式猜想尚未得到证明。在我的论文中，我提出了一个任意光滑流形上的函数代数的Hochschild上同调和同调复形的Fedosov决议。利用这些分解和Kontsevich关于R[[y_1，>..]的Hochschild上链的形式拟同构，y_d]]和Shoikhet的形式拟同构证明了任意光滑流形上函数代数的Hochschild链的Tsygan形式猜想. Hochschild链的形式拟同构的构造对于对（M，\nabla）的同构显然是函子的，其中M是流形，\nabla是切丛上的仿射联络.本文将这些结果应用于等变量子化、量子代数的霍赫希尔德同调的计算以及形变量子化中迹的描述。
Isoperimetric inequalities and the Friedlander-Milnor conjecture
本文证明了Friedlander关于代数群上同调的广义同构猜想，进而证明了离散复代数李群G（C）上同调的同构猜想，等价于G（F）的同调棒复形中存在一个等周不等式，其中F是有限域的代数闭包.
Model theoretic reformulation of the Baum-Connes and Farrell-Jones conjectures
同构猜想被翻译成同伦代数的语言，在那里它们类似于埃里森的下降定理。
Let $G$ be a group and let $E$ be a functor from small $\Z$-linear categories to spectra. Also let $A$ be a ring with a $G$-action. Under mild conditions on $E$ and $A$ one can define an equivariant homology theory of $G$-simplicial sets $H^G(-,E(A))$ with the property that if $H\subset G$ is a subgroup, then \[ H^G_*(G/H,E(A))=E_*(A\rtimes H) \] If now $\cF$ is a nonempty family of subgroups of $G$, closed under conjugation and under subgroups, then there is a model category structure on $G$-simplicial sets such that a map $X\to Y$ is a weak equivalence (resp. a fibration) if and only if $X^H…
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