-homotopy and refinement of observation. II: Adding new -homotopy equivalences.
Taylor towers of symmetric and exterior powers
We study the Taylor towers of the nth symmetric and exterior power functors, Spⁿ and Λⁿ. We obtain a description of the layers of the Taylor towers, and , in terms of the first terms in the Taylor towers of and for t < n. The homology of these first terms is related to the stable derived functors (in the sense of Dold and Puppe) of and . We use stable derived functor calculations of Dold and Puppe to determine the lowest nontrivial homology groups for and .
The Boardman category of spectra, chain complexes and (co)-localizations.
The branching nerve of HDA and the Kan condition.
The category of long exact sequences and the homotopy exact sequence of modules.
The cohomology ring of free loop spaces.
The construction of 3-Lie 2-algebras
We construct a 3-Lie 2-algebra from a 3-Leibniz algebra and a Rota-Baxter 3-Lie algebra. Moreover, we give some examples of 3-Leibniz algebras.
The equivalence of -groupoids and crossed complexes
The equivalence of -groupoids and cubical -complexes
The Euler characteristic of a category.
The Exponential Law of Maps. II.
The fundamental group of balanced simplicial complexes and posets.
The homology of tensor products [Book]
The homology of Ω(X v Y).
The homotopy category of chain complexes is a homotopy category
The Künneth Formula in Cyclic Homology.
The moduli space of n tropically collinear points in Rd.
The tropical semiring (R, min, +) has enjoyed a recent renaissance, owing to its connections to mathematical biology as well as optimization and algebraic geometry. In this paper, we investigate the space of labeled n-point configurations lying on a tropical line in d-space, which is interpretable as the space of n-species phylogenetic trees. This is equivalent to the space of n x d matrices of tropical rank two, a simplicial complex. We prove that this simplicial complex is shellable for dimension...
The S1-CW decomposition of the geometric realization of a cyclic set
We show that the geometric realization of a cyclic set has a natural, -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and -equivariant Borel homology of its geometric realization.
The tropical Grassmannian.
The universal functorial Lefschetz invariant
We introduce the universal functorial Lefschetz invariant for endomorphisms of finite CW-complexes in terms of Grothendieck groups of endomorphisms of finitely generated free modules. It encompasses invariants like Lefschetz number, its generalization to the Lefschetz invariant, Nielsen number and -torsion of mapping tori. We examine its behaviour under fibrations.