We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a CalabiYau target space are described b...

We study topological D-branes of type B in N = 2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described mathematically in terms of a triangulated category. For example, it has been argued that B-branes for an N = 2 sigma-model with a CalabiYau target space are described b...

Elmendorf’s Theorem in equivariant homotopy theory states that for any topological group G, the model category of G-spaces is Quillen equivalent to the category of continuous diagrams of spaces indexed by the opposite of the orbit category of G with the projective model structure. For discrete G, Bert Guillou explored equivariant homotopy theory for any cofibrantly generated model category C an...

We define a notion of weak cubical category, abstracted from the structure of n-cubical cospans x : ∧ → X in a category X, where ∧ is the ‘formal cospan’ category. These diagrams form a cubical set with compositions x +i y in all directions, which are computed using pushouts and behave ‘categorically’ in a weak sense, up to suitable comparisons. Actually, we work with a ‘symmetric cubical struc...

Cattani–Sassone’s notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled n-cube turns out to be the free higher dimensional transition system generated by one n-dimensional...

We define a notion of weak cubical category, abstracted from the structure of n-cubical cospans x : ∧ → X in a category X, where ∧ is the ‘formal cospan’ category. These diagrams form a cubical set with compositions x +i y in all directions, which are computed using pushouts and behave ‘categorically’ in a weak sense, up to suitable comparisons. Actually, we work with a ‘symmetric cubical struc...

In [2], working in the category of compactly generated spaces U , Elmendorf relates the equivariant homotopy theory of G-spaces to a homotopy theory of diagrams using fixed point sets. The diagrams are indexed by a topological category OG with objects the orbit spaces {G/H}H for the closed subgroups H ⊂ G. Although, his general assumption there is that G is a compact Lie group, a formulation of...

I work in an area at the intersection of representation theory, low-dimensional topology, higher category theory, and operator algebras which is often referred to as quantum algebra or quantum topology. A practical description of this field is that it consists of the mathematics which is descended from the Jones polynomial [Jon85]. The unifying idea behind quantum topology is to consider a func...

The strong shape category of topological spaces SSh can be defined using the coherent homotopy category CH, whose objects are inverse systems consisting of topological spaces, indexed by cofinite directed sets. In particular, if X, Y are spaces and q : Y → Y is a cofinite HPol-resolution of Y , then there is a bijection between the set SSh(X, Y ) of strong shape morphisms F : X → Y and the set ...