Related papers: Model and Set-Theoretic Aspects of Exotic Smoothne…

We introduce a variant of contact homology for convex open contact manifolds. As an application, we prove the existence of (in fact, infinitely many) exotic tight contact structures on $\mathbb{R}^{2n-1}$ for all $n>2$.

We study the dependence of the embedding calculus Taylor tower on the smooth structures of the source and target. We prove that embedding calculus does not distinguish exotic smooth structures in dimension 4, implying a negative answer to a…

We construct families of exotic spin-1/2 chains using a procedure called ``hard rod deformation''. We treat both integrable and non-integrable examples. The models possess a large non-commutative symmetry algebra, which is generated by…

In this thesis I present my research on the exotic configurations of antiferromagnetic systems characterised by a topological invariant. The research presented outlines the construction of novel local antiferromagnetic degrees of freedom…

Deformational structures, in many aspects generalizing standard elasticity theory, are investigated in abstract form. Within free deformational structures we define algebra of deformations, classify them by its special properties, define…

The recently discovered fourth class of Frobenius manifolds by Combe--Manin in opened and highlighted new geometric domains to explore. The guiding mantra of this article is to show the existence of hidden geometric aspects of the fourth…

Molodstov[10] introduced soft set theory as a new mathematical approach for solving problems having uncertainties. Many researchers worked on the findings of structures of soft set theory and applied to many problems having uncertainties.…

Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em each endomorphism…

This paper is devoted to the study of Poisson structures on the Euclidean four dimensional space R4. By using the properties of the trace operator associated to a volumen form and the elementary vector calculus operations in R3, we give…

We associate a homotopy Poisson-n algebra to any higher symplectic structure, which generalizes the common symplectic Poisson algebra of smooth functions. This provides robust n-plectic prequantum data for most approaches to quantization.…

We study the geometry and topology of exotic Springer fibers for orbits corresponding to one-row bipartitions from an explicit, combinatorial point of view. This includes a detailed analysis of the structure of the irreducible components…

To a system of second order ordinary differential equations (SODE) one can assign a canonical nonlinear connection that describes the geometry of the system. In this work we develop a geometric setting that allows us to assign a canonical…

The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group $G$ with relations. A valid subgroup $H$ of index $d$ in $G$ leads to a 'magic' state…

Ruberman in the 90's showed that the group of exotic diffeomorphisms of closed 4-manifolds can be infinitely generated. We provide various results on the question of when such infinite generation can localize to a smaller embedded…

Topological quantum matter exhibits a range of exotic phenomena when enriched by subdimensional symmetries. This includes new features beyond those that appear in the conventional setting of global symmetry enrichment. A recently discovered…

We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to…

Using an obstruction based on Donaldson's theorem, we derive strong restrictions on when a Seifert fibered space $Y = F(e; \frac{p_1}{q_1}, \ldots, \frac{p_k}{q_k})$ over an orientable base surface $F$ can smoothly embed in $S^4$. This…

The important unsolved problem in theory of integrable systems is to find conditions guaranteeing existence of a Lax representation for a given PDE. The use of the exotic cohomology of the symmetry algebras opens a way to formulate such…

We give an infinite family of embeddings of $\mathbb{R} P^2$ to $S^4$ such that they are mutually topologically isotopic however are not smoothly isotopic to each other. Moreover, they are topologically isotopic to the standard $P^2$-knot.…

The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of…