Related papers: Mather invariants in groups of piecewise-linear ho…
In his earlier work, the author introduced a group theory question that arises in the study of iterated Galois groups of post-critically finite quadratic polynomials. In this paper, we prove the first non-trivial results on this question.
We describe a connected component of the space of conjugacy classes of representations of the modular group $\mathrm{PSL}_2(\mathbb{Z})$ into the isometry group of the symmetric space $\mathrm{SL}_3(\mathbb{R})/\mathrm{SO}(3)$. This…
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Gra\~na. We specialize that theory to the case when there is a group action on the coefficients. First,…
We construct homeomorphisms of compacta from relations between finite graphs representing their open covers. Applied to the pseudoarc, this yields simple Fra\"iss\'e theoretic proofs of several important results, both old and new.…
Let $\Diffeo=\Diffeo(\R)$ denote the group of infinitely-differentiable diffeomorphisms of the real line $\R$, under the operation of composition, and let $\Diffeo^+$ be the subgroup of diffeomorphisms of degree +1, i.e.…
Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…
In their paper on multivariable dynamics, Davidson and Katsoulis conjectured that two multivariable dynamical systems have isomorphic tensor algebras if and only if they are piecewise conjugate. We disprove the conjecture by constructing…
In this paper we develop unifying graph theoretic techniques to study the dynamics and the structure of the space of homeomorphisms and the space of self-maps of the Cantor space. Using our methods, we give characterizations which determine…
Over a field of characteristic 0, the algebra of invariants of several $n\times n$ matrices under simultameous conjugation by $GL_n$ is generated by traces of products of generic matrices. Teranishi, 1986, found a minimal system of eleven…
We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov's first and second Poincare duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz…
A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that $\eta_i:\X_i\to \X_i$ is a continuous proper map on a locally compact…
We describe a new way to relate an acyclic, skew-symmetrizable cluster algebra to the representation theory of a finite dimensional hereditary algebra. This approach is designed to explain the c-vectors of the cluster algebra. We obtain a…
The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group…
We consider quivers/skew-symmetric matrices under the action of mutation (in the cluster algebra sense). We classify those which are isomorphic to their own mutation via a cycle permuting all the vertices, and give families of quivers which…
The toric manifolds in question were invented by Bott and studied by Grossberg and Karshon under the name "Bott towers". Interest in them comes from their relation to characters of semisimple Lie groups and geometric quantization. We offer…
We consider invariants of a finite group related to the number of random (independent, uniformly distributed) conjugacy classes which are required to generate it. These invariants are intuitively related to problems of Galois theory. We…
The investigation and classification of non-unique factorization phenomena have attracted some interest in recent literature. For finitely generated monoids, S.T. Chapman and P. Garcia-Sanchez, together with several co-authors, derived a…
We present a method to produce examples of non-homeomorphic conjugate complex varieties based on the genus theory of lattices. As an application, we give examples of arithmetic Zariski pairs.
We compute Joyce's (arXiv:2111.04694) enumerative invariants $[\mathcal{M}^{\mathrm{ss}}_{(r,d)}]_{\mathrm{inv}}$ for semistable rank $r$ degree $d$ coherent sheaves on a complex projective curve. These invariants are a generalization of…
In this paper we explore relationships between divergence and thick groups, and with the same techniques we estimate lengths of shortest conjugators. We produce examples, for every positive integer n, of CAT(0) groups which are thick of…