Related papers: Linearisation of conservative toral homeomorphisms
Following the argument for diffeomorphisms by Galatius and Randal-Williams, we prove that homeomorphisms of 1-connected manifolds of even dimension at least 6 exhibit homological stability. We deduce similar results for PL homeomorphisms…
We show that, for pairs of hyperbolic toral automorphisms on the $2$-torus, the points with dense forward orbits under one map and nondense forward orbits under the other is a dense, uncountable set. The pair of maps can be noncommuting. We…
We suggest a geometrical approach to the semi-invariants of quivers based on Luna's slice theorem and the Luna-Richardson theorem. The locally semi-simple representations are defined in this spirit but turn out to be connected with stable…
We characterize the seminormality of an affine semigroup ring in terms of the dualizing complex, and the normality of a Cohen-Macaulay semigroup ring by the "shape" of the canonical module. We also characterize the seminormality of a toric…
We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and…
We study homological mirror symmetry for not necessarily compactly supported coherent sheaves on the minimal resolutions of A_n-singularities. An emphasis is put on the relation with the Strominger-Yau-Zaslow conjecture.
We explore the relation of weak conjugacy in the group of homeomorphisms isotopic to the identity, for surfaces.
Let S be a compact connected surface and let f be an element of the group Homeo\_0(S) of homeomorphisms of S isotopic to the identity. Denote by \tilde{f} a lift of f to the universal cover of S. Fix a fundamental domain D of this universal…
It is shown that max-preserving maps (or join-morphisms) on the positive orthant in Euclidean $n$-space endowed with the component-wise partial order give rise to a semiring. This semiring admits a closure operation for maps that generate…
We study cocycles of homeomorphisms of $\T$ in the isotopy class of the identity over shift spaces, using as a tool a novel definition of rotation sets inspired in the classical work of Miziurewicz and Zieman. We discuss different notions…
We augment the method of $C^\infty$ conjugation approximation with explicit estimates on the conjugacy map. This allows us to construct ergodic volume preserving diffeomorphisms measure-theoretically isomorphic to any apriori given…
We observe that if we are interested primarily in degeneration arguments, there is a weaker notion of (semi)stability for vector bundles on reducible curves, which is sufficient for many applications, and does not depend on a choice of…
We study a notion of potential isomorphism, where two structures are said to be potentially isomorphic if they are isomorphic in some generic extension that preserves stationary sets and does not add new sets of cardinality less than the…
We give a necessary and sufficient condition for the orientability of a locally standard 2-torus manifold with a fixed point which generalizes previous results of Nakayama-Nishimura in 2005 and Soprunova-Sottile in 2013. We construct…
This survey gives a unified treatment of topics from Abelian and non-Abelian Nielsen Theory integrated with the semiconjugacy theorems of Franks and Handel. The main focus is to develop an analog of the rotation set that is valid when the…
We show that the rotation algebras are limit of matrix algebras in a very strong sense of convergence for algebras with additional Lipschitz structure. Our results generalize to higher dimensional noncommutative tori and operator valued…
We classify spin structures on the noncommutative torus, and find that the noncommutative n-torus has 2^n spin structures, corresponding to isospectral deformations of spin structures on the commutative n-torus. For n>3 the classification…
We develop a rotational hyperbolic theory for surface homeomorphisms. We use the equivalence relation on ergodic measures that have nontrivial rotational behaviour defined in [arXiv:2312.06249] to define a rotational counterpart of…
We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued fraction of the rational tangle. Furthermore, we generalize…
We study a parametric family of piecewise rotations of the torus, in the limit in which the rotation number approaches the rational value 1/4. There is a region of positive measure where the discontinuity set becomes dense in the limit; we…