Related papers: Non ambiguous structures on 3-manifolds and quantu…
Torsion polynomials connect the genus of a hyperbolic knot (a topological invariant) with the discrete faithful representation (a geometric invariant). Using a new combinatorial structure of an ideal triangulation of a 3-manifold that…
4-manifolds have special topological properties which can be used to get a different view on quantum mechanics. One important property (connected with exotic smoothness) is the natural appearance of 3-manifold wild embeddings (Alexanders…
The main result of this paper is that any $3$-dimensional manifold with a finite group action is equivariantly, invertibly homology cobordant to a hyperbolic manifold; this result holds with suitable twisted coefficients as well. The…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
We introduce the notion of infinitesimal variations of mixed Hodge structures and invariants associated to them. We describe these invariants in the case of a pair $(X,Y)$ with $X$ a Fano 3-fold and $Y$ a smooth anticanonical K3 surface and…
In the definition of irreducible holomorphic symplectic manifolds the condition of being simply connected can be replaced by vanishing irregularity. We discuss finite quotients X of complex tori where the space of reflexive 2-forms is…
Defects on the toric code, a well-known exactly solvable Abelian anyon model, can exhibit non-Abelian statistical properties, which can be classified into punctures and twists. Benhemou et al.[Phys. Rev. A. 105, 042417 (2022)] introduced a…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
Classical work of Thurston and Gabai shows that finitely many taut sutured manifold hierarchies determine the Thurston norm of a compact oriented irreducible $3$-manifold with toroidal boundary. We give an explicit procedure to extract this…
On one side, from the properties of Floer cohomology, invariant associated to a symplectic manifold, we define and study a notion of symplectic hyperbolicity and a symplectic capacity measuring it. On the other side, the usual notions of…
We describe the mathematical theory of topological quantum computing with symmetry defects in the language of fusion categories and unitary representations. Symmetry defects together with anyons are modeled by G-crossed braided extensions…
The crystal symmetry of a material dictates the type of topological band structures it may host, and therefore symmetry is the guiding principle to find topological materials. Here we introduce an alternative guiding principle, which we…
We construct a simple topological invariant of certain 3-manifolds, including quotients of the 3-sphere by finite groups, based on the fact that the tangent bundle of an orientable 3-manifold is trivialisable. This invariant is strong…
Using results relating taut foliations and pseudo-Anosov flows, we find cusped hyperbolic 3-manifolds which are not the non-singular part of a pseudo-Anosov flow. In particular, we find the first examples of cusped hyperbolic 3-manifolds…
We prove the Turaev-Viro invariants volume conjecture for a "universal" class of cusped hyperbolic 3-manifolds that produces all 3-manifolds with empty or toroidal boundary by Dehn filling. This leads to two-sided bounds on the volume of…
We show that the superconformal symmetries of the (1,1) sigma model decompose into a set of more refined symmetries when the target space admits projectors $P_{\pm}$, and the orthogonal complements $Q_{\pm}$, covariantly constant with…
This Letter shows that a supersymmetric structure is inherent to the time space inverted (TSI) quantum mechanics (QM) framework, where the spatial evolution of states is generated by the operator…
Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$ taken from some parameter space $M$. We demonstrate how all geometric properties of this manifold of states are fully described by a scalar gauge-invariant Bargmann…
This paper continues our exploration of homology cobordism of 3-manifolds using our recent results on Cheeger-Gromov rho-invariants associated to amenable representations. We introduce a new type of torsion in 3-manifold groups we call…
We use our new type of bounded locally homeomorphic quasiregular mappings in the unit 3-ball to address long standing problems for such mappings. The construction of such mappings comes from our construction of non-trivial compact…