Related papers: Inca Foams
We introduce a relation of cobordism for knots in thickened surfaces and study cobordism invariants of such knots.
We show that a regular isomorphism of profinite completion of the fundamental groups of two 3-manifolds $N_1$ and $N_2$ induces an isometry of the Thurston norms and a bijection between the fibered classes. We study to what extent does the…
The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative…
With any integral lattice \Lambda in n-dimensional euclidean space we associate an elementary abelian 2-group I(\lambda) whose elements represent parts of the dual lattice that are similar to \Lambda. There are corresponding involutions on…
In the first part of the paper we survey several results from Popa's deformation/rigidity theory on the classification of tensor product decompositions of large natural classes of II$_1$ factors. Using a m\'elange of techniques from…
We extend the entanglement bootstrap approach to (3+1)-dimensions. We study knotted excitations of (3+1)-dimensional liquid topological orders and exotic fusion processes of loops. As in previous work in (2+1)-dimensions, we define a…
This is the first in a series of papers where scissor congruence and K-theoretical invariants are related to cobordism groups of foams in various dimensions. A model example is provided where the cobordism group of weighted one-foams is…
There exists a smooth foliation with 3 singular points on the two-dimensional torus such that any lifting of a leaf of this foliation on the universal covering of the torus is a dense subset of the covering.
We consider free surface instabilities of films flowing on inverted substrates within the framework of lubrication approximation. We allow for the presence of fronts and related contact lines, and explore the role which they play in…
Thin elastic two-dimensionnal systems under compressive stresses may relieve part of their stretching energy by developing out of plane undulations. We investigate experimentally and theoretically the indentation of an elastic disk…
We construct invariants of colored links using equivariant bordism groups of Conner and Floyd. We employ this bordism invariant to find the first examples of topological vortex knots, the knot structure of which is protected from decaying…
Two-dimensional second-order topological insulators are characterized by the presence of topologically protected zero-energy bound states localized at the corners of a flake. In this paper we theoretically study the occurrence and features…
We present a study of narrow filaments toward a massive infrared dark cloud, NGC 6334S, using the Atacama Large Millimeter/submillimeter Array (ALMA). Thirteen gas filaments are identified using the H$^{13}$CO$^{+}$ line, while a single…
In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated…
We propose a new method of computing cohomology groups of spaces of knots in $\R^n$, $n \ge 3$, based on the topology of configuration spaces and two-connected graphs, and calculate all such classes of order $\le 3.$ As a byproduct we…
We establish the duality between the torus knot superpolynomials or the Poincar\'e polynomials of the Khovanov homology and particular condensates in $\Omega$-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS)…
In this paper we use the connected sum operation on knots to show that there is a one-to-one relation between knots and numbers. In this relation prime knots are bijectively assigned with prime numbers such that the prime number 2…
We classify genus-two L-space knots in the Poincar\'e homology sphere. This leads to the second knot Floer homology detection result for a knot of genus at least two, and the first such result outside of $S^3$. The argument uses the theory…
We prove that if two conformal embeddings between Riemann surfaces with finite topology are homotopic, then they are isotopic through conformal embeddings. Furthermore, we show that the space of all conformal embeddings in a given homotopy…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…