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2-Quasi Crossed Modules of Commutative Algebras
We define 2-quasi crossed modules of commutative algebras obtained by relaxing some 2-crossed module conditions. Moreover, we prove that there exists...
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Crossed Modules of Monoids III. Simplicial Monoids of Moore Length 1
This is the last part of a series of three strongly related papers in which three equivalent structures are studied:
Internal categories in categories...
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Cubulating Coxeter Groups
Coxeter groups are abstract versions of reflection groups. They are widely studied in many areas of mathematics and play a central role in geometric...
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Congruence Normality of Simplicial Hyperplane Arrangements via Oriented Matroids
A catalogue of simplicial hyperplane arrangements was first given by Grünbaum in 1971. These arrangements naturally generalize finite Coxeter...
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Bounded and unbounded cohomology of homeomorphism and diffeomorphism groups
We determine the bounded cohomology of the group of homeomorphisms of certain low-dimensional manifolds. In particular, for the group of...
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Crossed Modules of Monoids II: Relative Crossed Modules
This is the second part of a series of three strongly related papers in which three equivalent structures are studied:
Internal categories in...
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On the Second Homology of Crossed Modules
In this article, we present a new description of the integral second homology of crossed modules of groups and generalize two basic results on the...
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Right exact localizations of groups
We introduce several classes of localizations (idempotent monads) on the category of groups and study their properties and relations. The most...
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Crossed Modules of Monoids I: Relative Categories
This is the first part of a series of three strongly related papers in which three equivalent structures are studied:
internal categories in...
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Reflection Groups and Coxeter Groups
We explain why reflection groups are Coxeter groups. This motivates the general definition of Coxeter groups. We also explain the geometric meaning...
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Cyclic Sets
We know that it is not possible to directly equip a simplicial set with a compact Lie group action. However, for some groups G, it is possible to...
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Other Cohomologies
The chapter begins by comparing the \(\mathsf {D}\)...
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Homology Groups of Cubical Sets with Connections
Toward defining commutative cubes in all dimensions, Brown and Spencer introduced the notion of “connection” as a new kind of degeneracy. In this...
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Median quasimorphisms on \({{\,\mathrm{{CAT}}\,}}(0)\) cube complexes and their cup products
Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks...
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Special cubulation of strict hyperbolization
We prove that the Gromov hyperbolic groups obtained by the strict hyperbolization procedure of Charney and Davis are virtually compact special, hence...
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Volume and macroscopic scalar curvature
We prove the macroscopic cousins of three conjectures: (1) a conjectural bound of the simplicial volume of a Riemannian manifold in the presence of a...
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Sullivan’s Juvenilia: Surgery and Algebraic Topology
Dennis Sullivan’s early work, despite being strongly motivated by geometric problems, had a strong algebraic nature, certainly much more so than his...
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A comonadic interpretation of Baues–Ellis homology of crossed modules
We introduce and study a homology theory of crossed modules with coefficients in an abelian crossed module. We discuss the basic properties of these...