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The purpose of this paper is to put together a large amount of results on the $K (π, 1)$ conjecture for Artin groups, and to make them accessible to non-experts. Firstly, this is a survey, containing basic definitions, the main results, examples and an historical overview of the subject. But, it is also a reference text on the topic that contains proofs of a large part of the results on this question. Some proofs as well as few results are new. Furthermore, the text, being addressed to non-experts, is as...

Kan fibrations in the category of simplicial spaces

R. Seymour (1980)

Fundamenta Mathematicae

Kann fibrations which are homomorphisms of simplicial groups

C. Ruiz Salguero, R. Ruiz (1973)

Revista colombiana de matematicas

Kann-Bedingungen und abstrakte Homotopietheorie.

Klaus Heiner Kamps (1972)

Mathematische Zeitschrift

Karoubi’s relative Chern character and Beilinson’s regulator

Georg Tamme (2012)

Annales scientifiques de l'École Normale Supérieure

We construct a variant of Karoubi’s relative Chern character for smooth varieties over $𝐂$ and prove a comparison result with Beilinson’s regulator with values in Deligne-Beilinson cohomology. As a corollary we obtain a new proof of Burgos’ Theorem that for number fields Borel’s regulator is twice Beilinson’s regulator.

Kazhdan-Lusztig Conjecture and Holonomic Systems.

M. Kashiwara, J.L. Brylinski (1981)

Inventiones mathematicae

Khovanov homology, its definitions and ramifications

Oleg Viro (2004)

Fundamenta Mathematicae

Mikhail Khovanov defined, for a diagram of an oriented classical link, a collection of groups labelled by pairs of integers. These groups were constructed as the homology groups of certain chain complexes. The Euler characteristics of these complexes are the coefficients of the Jones polynomial of the link. The original construction is overloaded with algebraic details. Most of the specialists use adaptations of it stripped off the details. The goal of this paper is to overview these adaptations...

Khovanov's homology for tangles and cobordisms.

Bar-Natan, Dror (2005)

Geometry & Topology

Killing vectors and geodesic flow vectors on tangent bundles.

Shukichi Tanno (1976)

Journal für die reine und angewandte Mathematik

k-Invariants of knotted 2-spheres.

S.P. Plotnick, A. I. Suciu (1985)

Commentarii mathematici Helvetici

KKM maps and variational inequalities

J. Dugundji, A. Granas (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Knit products of graded Lie algebras and groups

Michor, Peter W. (1990)

Proceedings of the Winter School "Geometry and Physics"

Let $A = ⨁_{k} A_{k}$ and $B = ⨁_{k} B_{k}$ be graded Lie algebras whose grading is in $𝒵$ or $𝒵_{2}$ , but only one of them. Suppose that $(α, β)$ is a derivatively knitted pair of representations for $(A, B)$ , i.e. $α$ and $β$ satisfy equations which look “derivatively knitted"; then $A \oplus B : = ⨁_{k, l} (A_{k} \oplus B_{l})$ , endowed with a suitable bracket, which mimics semidirect products on both sides, becomes a graded Lie algebra $A \oplus_{(α, β)} B$ . This graded Lie algebra is called the knit product of $A$ and $B$ . The author investigates the general situation for any graded Lie subalgebras $A$ and $B$ of a graded...

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K (2)- homology of some infinite loop spaces.

$K$ - and $L$ -theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by $ℤ / 4$ .

$K$ -théorie algébrique et représentations de groupes

$K$ -theory of oriented Grassmann manifolds

$K (π, 1)$ conjecture for Artin groups