This paper is a survey of new results and open problems connected with fundamental
combinatorial concepts, including polytopes, simplicial complexes, cubical complexes, and …

Here, the study of torus actions on topological spaces is presented as a bridge connecting
combinatorial and convex geometry with commutative and homological algebra, algebraic …

A torus manifold is an even-dimensional manifold acted on by a half-dimensional torus with
non-empty fixed point set and some additional orientation data. It may be considered as a far …

Our aim is to bring the theory of analogous polytopes to bear on the study of quasitoric
manifolds, in the context of stably complex manifolds with compatible torus action. By way of …

A Bott tower is the total space of a tower of fibre bundles with base and fibres. Every Bott
tower of height n is a smooth projective toric variety whose moment polytope is …

We argue for the addition of category theory to the toolkit of toric topology, by surveying
recent examples and applications. Our case is made in terms of toric spaces X_K, such as …

For several important classes of manifolds acted on by the torus, the information about the
action can be encoded combinatorially by a regular n-valent graph with vector labels on its …

Quasitoric spaces were introduced by Davis and Januskiewicz in their 1991 Duke paper.
There they extensively studied topological invariants of quasitoric manifolds. These …

For each strongly connected finite-dimensional (pure) simplicial complex Δ we construct a
finite group Π(Δ), the group of projectivities of Δ, which is a combinatorial but not a …

Our primary aim is to develop a theory of equivariant genera for stably complex manifolds
equipped with compatible actions of a torus T k. In the case of omnioriented quasitoric …