Configuration Spaces and Polyhedral Products

This paper aims to find the most general combinatorial conditions under which a moment-angle complex $(D^2,S^1)^K$ is a co-$H$-space, thus splitting unstably in terms of its full subcomplexes. In this way we study to which extent the conjecture holds that a moment-angle complex over a Golod simplicial complex is a co-$H$-space. Our main tool is a certain generalisation of the theory of labelled configuration spaces.Comment: Published in Advances in Mathematics, 201

The homotopy type of the polyhedral product for shifted complexes

We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices,X1,...,Xn are pointed connected CW-complexes and CXi is the cone on Xi, then the polyhedral product determined by K and the pairs (C Xi , Xi ) is homotopy equivalent to a wedge of suspensions of smashes of the Xi ’s. Earlier work of the authors dealt with the special case where each Xi is a loop space. New techniques are introduced to prove the general case. These have the advantage of simplifying the earlier results and of being sufficiently general to show that the conjecture holds for a substantially larger class of simplicial complexes. We discuss connections between polyhedral products and toric topology, combinatorics, and classical homotopy theory

LSLS-Category of Moment-Angle Manifolds, Massey Products, and a Generalization of the Golod Property

We give various bounds for the Lusternik-Schnirelmann category of moment-angle complexes and show how this relates to vanishing of Massey products in $\mathrm{Tor}^+_{R[v_1,\ldots,v_n]}(R[K],R)$. In particular, we characterise the Lusternik-Schnirelmann category of moment-angle manifolds $\mathcal{Z}_K$ over triangulated $d$-spheres $K$ for $d\leq 2$, as well as higher dimension spheres built up via connected sum, join, and vertex doubling operations. This characterisation is given in terms of the combinatorics of $K$, the cup product length of $H^*(\mathcal{Z}_K)$, as well as a certain generalisation of the Golod property. Some applications include information about the category and vanishing of Massey products for moment-angle complexes over fullerenes and $k$-neighbourly complexes.Comment: New examples adde

Applications of combinatorial groups to Hopf invariant and the exponent problem

Combinatorial groups together with the groups of natural coalgebra transformations of tensor algebras are linked to the groups of homotopy classes of maps from the James construction to a loop space. This connection gives rise to applications to homotopy theory. The Hopf invariants of the Whitehead products are studied and a rate of exponent growth for the strong version of the Barratt Conjecture is given.Comment: This is the version published by Algebraic & Geometric Topology on 29 November 200

The Thracian Hero on the Danube New Interpretation of an Inscription from Diana

The paper looks at some aspects of the Thracian Hero cult on the Danube frontier of Upper Moesia inspired by a reinterpretation of a Latin votive inscription from Diana, which, as the paper proposes, was dedicated to Deo Totovitioni. Based on epigraphic analogies, the paper puts forth the view that it was a dedication to the Thracian Hero, since it is in the context of this particular cult that the epithet Totovitio has been attested in various variants (Toto-viti- / Toto-bisi- / Toto-ithi-)

Augustan Conquest of the Balkans in the Light of Triumphal Monuments

The article offers an interpretation of inscriptions from the Sebasteion of Aphrodisias in Caria that represent Roman victories in the Balkans during the reign of Augustus. Six inscriptions from sc. ἔθνη series commemorate Danubian-Balkan tribes: Japodes Andizetes, Pirustae, Dardani, Dacians, Bessi. These monuments provide not only early epigraphic attestations of single tribes but seem to illuminate, to some extent, the rôle that pacification of the Danubian-Balkan regions played in Augustan propagandic imagery