Related papers: Twisted Arrow Construction for Segal Spaces
Casual structure can take the form of cone bundles on a manifold, more general local preorders on a topological space, or simplicial orientations implicit in a simplicial set. This note takes a triangulation of a conal manifold M to mean an…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
We describe a notion of (abstract) projective line over a field as a set equipped with a certain first order structure, and a projectivity between projective lines as a bijection preserving this structure. The structure in question is that…
In the present notes we introduce and study the twisted gamma-filtration on K_0(G), where G is a split simple linear algebraic group over a field of characteristic prime to the order of the center of G. We apply this filtration to construct…
Twist tori are examples of exotic monotone lagrangian tori, presented in [1]. This tree of examples grew up over the first one --- the torus $\Theta \in \R^4$, constructured in [2] and [3]. On the other hand, in [4] and [5] we proposed a…
Target space duality symmetries, which acts on K\"ahler and continuous Wilson line moduli, of a ${\bf Z}_N$ ($N\not=2$) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These…
This paper describes some algebraic properties of the species of finite topological quandles. We construct two twisted bialgebra structures on this species, one of the first kind and one of the second kind. The obstruction for the structure…
In this paper, we introduce the notion of bigraft algebra, generalizing the notions of left and right graft algebras. We give a combinatorial description of the free bigraft algebra generated by one generator and we endow this algebra with…
The recently introduced anomaly-free twistor string in four dimensions is shown to be defined not just in flat but also in curved twistor space. Further, arguments are given that the classical limit of the corresponding string field theory,…
Every (left) linear function on a subspace of a finite-dimensional vector space over a (skew) field can be extended to a (left) linear function on the whole space. This paper explores the extent to what this basic fact of linear algebra is…
We define algebras of admissible functions associated to twisted Dirac structures, and we show that they are Poisson algebras. We study the standard cases associated to Dirac structures defined by graphs of non-degenerate 2-forms.
Twisted bilayer graphene exhibits electronic properties that are highly correlated with the size and arrangement of moir\'e patterns. While rigid rotation of two layers creates the topology of moir\'e patterns, local rearrangements of the…
A "reduced" differential geometry adapted to the presence of abelian isometries is constructed.Classical T-duality diagonalizes in this setting, allowing us to get conveniently the transformation of the relevant geometrical objects such as…
A rich zoology of shapes emerges from a simple stretched and twisted elastic ribbon. Despite a lot of interest, all these shape are not understood, in particular the shape that prevails at large tension and twist and that emerges from a…
We introduce the notion of a twisted differential operator of given radius relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism $$\sigma$$. As…
An important result in real algebraic geometry is the projection theorem: every projection of a semialgebraic set is again semialgebraic. This theorem and some of its conclusions lie at the basis of many other results, for example the…
We present experimental measurements on the spontaneous formation of compact spiral structures in vertically-vibrated granular chains. Under weak vibration, when the chain is quasi two-dimensional and self-avoiding, spiral structures emerge…
Including {\it world-sheet orientation-reversing automorphisms} $\hat{h}_{\sigma} \in H_-$ in the orbifold program, we construct the operator algebras and twisted KZ systems of the general WZW {\it orientation orbifold} $A_g (H_-) /H_-$. We…
We study the application of IBL-infinity-algebras to string topology and explicitly compute the case of spheres. This involves finding a Green kernel and computing integrals associated to trivalent ribbon graphs, which are similar to…
Freer monads are a useful structure commonly used in various domains due to their expressiveness. However, a known issue with freer monads is that they are not amenable to static analysis. This paper explores freer arrows, a relatively…