Related papers: The Topological Period-Index Problem over 8-Comple…

The space K^n of all n-dimensional { Lie} algebras has a natural non-Hausdorff topology k^n, which has characteristic limits, called transitions, A -> B, between distinct Lie algebras A and B. The entity of these transitions are the natural…

Nonsymmorphic symmetries can enforce band connectivity that obstructs a single-band Wannier description. We show that a fractional translation $\mathcal{L}$ connecting distinct high-symmetry Wyckoff positions generically renders the Wannier…

Poisson structures of the Poincar\'e group can be linked to deformations of the Minkowski space-time, classified some time ago by Zakrewski. Based on this classification, various quantum Minkowski space-times with coordinates Lie algebras…

A polynomial Turing compression (PTC) for a parameterized problem $L$ is a polynomial time Turing machine that has access to an oracle for a problem $L'$ such that a polynomial in the input parameter bounds each query. Meanwhile, a…

Among plenty of applications, low-dimensional homogeneous spaces appear in cosmological models as both, classical factor spaces of multidimensional geometry and minisuperspaces in canonical quantization. Here a new tool to restrict their…

In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We…

Hausmann and Rodriguez classified spaces of isometry classes of planar n-gons according to their genetic code, which is a collection of sets (called genes) containing n. Omitting the n yields what we call gees. We prove that, for a set of…

Let $M$ be a closed orientable $(n-1)$-connected $(2n+2)$-manifold, $n\geq 2$. In this paper we combine the Postnikov tower of spheres and the homotopy decomposition of the reduced suspension space $\Sigma M$ to investigate the cohomotopy…

In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band…

Recently Kontsevich solved the classification problem for deformation quantizations of all Poisson structures on a manifold. In this paper we study those Poisson structures for which the explicit methods of Fedosov can be applied, namely…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the…

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of…

In this work, we revisit the model of PbTe presented in [E. Fradkin, E. Dagotto, and D. Boyanovsky, Phys. Rev. Lett. 57, 2967 (1986)]. We show that the low energy theory of this model corresponds to a (higher-order) topological crystalline…

Kapustin-Witten (KW) equations are encountered in the localization of the topological N=4 SYM theory. Mikhaylov has constructed model solutions of KW equations for the boundary 't~Hooft operators on a half space. Direct proof of the…

The Petrov classification is an important algebraic classification for the Weyl tensor valid in 4-dimensional space-times. In this thesis such classification is generalized to manifolds of arbitrary dimension and signature. This is…

We find the limiting proportion of periodic points in towers of finite fields for polynomial maps associated to algebraic groups, namely pure power maps z^d and Chebyshev polynomials.

Three-dimensional, crystalline Hopf insulators are generic members of unitary Wigner-Dyson class, which can break all global discrete symmetries and point group symmetries. In the absence of first Chern number for any two-dimensional plane…

If $B$ is a toric manifold and $E$ is a Whitney sum of complex line bundles over $B$, then the projectivization $P(E)$ of $E$ is again a toric manifold. Starting with $B$ as a point and repeating this construction, we obtain a sequence of…

We give a complete classification of torsion pairs in repetitive cluster categories of type $A_n$, which were defined by Zhu as the orbit categories, via certain configurations of diagonals, called Ptolemy diagrams. As applications, we…