Related papers: The Homflypt polynomial and the oriented Thompson …

We define basic notions in the category of conic representations of a topological group and prove elementary facts about them. We show that a conic representation determines an ordinary dynamical system of the group together with a…

We study Hamiltonian and symplectic tensor structures in the T-product algebra. We define T-Hamiltonian and T-symplectic tensors and characterize them through their Fourier-domain slices. For T-Hamiltonian tensors we establish the standard…

Recently Vaughan Jones showed that the R. Thompson group $F$ encodes in a natural way all knots, and a certain subgroup $\vec F$ of $F$ encodes all oriented knots. We answer several questions of Jones about $\vec F$. In particular we prove…

Let K be the product O(n_1) x O(n_2) x ... x O(n_r) of orthogonal groups. Let V the r-fold tensor product of defining representations of each orthogonal factor. We compute a stable formula for the dimension of the K-invariant algebra of…

We solve the twisted conjugacy problem on Thompson's group F. We also exhibit orbit undecidable subgroups of Aut(F), and give a proof that Aut(F) and Aut_+(F) are orbit decidable provided a certain conjecture on Thompson's group T is true.…

We introduce the notion of a \emph{conic sequence} of a convex polytope. It is a way of building up a polytope starting from a vertex and attaching faces one by one with certain regulations. We apply this to a toric variety to obtain an…

Resolvent compositions were recently introduced as monotonicity-preserving operations that combine a set-valued monotone operator and a bounded linear operator. They generalize in particular the notion of a resolvent average. We analyze the…

We define series of representations of the Thompson's groups $F$ and $T$, which are analogs of principal series representations of $SL(2,\R)$. We show that they are irreducible and classify them up to unitary equivalence. We also prove that…

Let us consider the renormalized Nelson model at a fixed total momentum $P$: $H_{\mathrm{ren}}(P)$; The Hamiltonian $H_{\mathrm{ren}}(P)$ is defined through an infinite energy renormalization. We prove that $e^{-\beta H_{\mathrm{ren}}(P)}$…

Consider a source proper, source connected regular symplectic groupoid acting locally freely and effectively in a Hamiltonian way, and assume that the moment map is proper and has connected fibres. In this case there is an associated…

We present new results regarding automatic continuity, unifying some diagonalization concepts that have been developed over the years. For example, any homomorphism from a completely metrizable topological group to Thompson's group $F$ has…

For any tangle $T$ (up to isotopy) and integer $k\geq 1$ we construct a group $F(T)$ (up to isomorphism). It is the fundamental group of the configuration space of $k$ points in a horizontal plane avoiding the tangle, provided the tangle is…

In group representations several inductions given by tensoring with appropriate bimodules may be reconstructed via homology of $G$-posets with $G$-equivariant coefficients. For this purpose, we need various local categories of a finite…

We show that Martin Hyland's effective topos can be exhibited as the homotopy category of a path category $\mathbb{EFF}$. Path categories are categories of fibrant objects in the sense of Brown satisfying two additional properties and as…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

Polynomial invariants corresponding to the fundamental representation of the gauge group $SO(N)$ are computed for arbitrary torus knots in the framework of Chern-Simons gauge theory making use of knot operators. As a result, a formula which…

We prove a Thom isomorphism theorem for differential forms in the setting of transverse Lie algebra actions on foliated manifolds and foliated vector bundles.

We present definitions of homology groups associated to a family of amalgamation functors. We show that if the generalized amalgamation properties hold, then the homology groups are trivial. We compute the group H_2 for strong types in…

A spectral sequence calculating the homology groups of some spaces of maps equivariant under compact group actions is described. For the main example, we calculate the rational homology groups of spaces of even and odd maps $S^m \to S^M$,…

The main goal is to find the Homfly polynomial of a link formed by decorating each component of the Hopf link with the closure of a directly oriented tangle. Such decorations are spanned in the Homfly skein of the annulus by elements…