相关论文: Wild solenoids

The tenfold way is a classification scheme for the building blocks of free fermion systems. More precisely, it classifies the isomorphism classes of spaces of equivariant free Hamiltonians in irreducible fermion systems with symmetries.…

Let $G$ be a profinite group, $X$ a discrete $G$-spectrum with trivial action, and $X^{hG}$ the continuous homotopy fixed points. For any $N \trianglelefteq_o G$ ("$o$" for open), $X = X^N$ is a $G/N$-spectrum with trivial action. We…

A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible…

In this note, we study equivariant versions of Stolz' $R$-groups, the positive scalar curvature structure groups $R^{\rm spin}_n(X)^G$, for proper actions of discrete groups $G$. We define the concept of a fundamental groupoid functor for a…

If $G$ is a finite $\ell$-group acting on an affine space $\mathbb{A}^n$ over a finite field $K$ of cardinality prime to $\ell$, Serre has shown that there exists a rational fixed point. We generalize this to the case where $K$ is a…

We definitively establish that the theory of symmetric Macdonald polynomials aligns with quantum and affine Schubert calculus using a discovery that distinguished weak chains can be identified by chains in the strong (Bruhat) order poset on…

In this paper we investigate relations between Koopman, groupoid and quasi-regular representations of countable groups. We show that for an ergodic measure class preserving action of a countable group G on a standard Borel space the…

Under non-commutative Stone duality, there is a correspondence between second countable Hausdorff \'etale groupoids which have a Cantor space of identities and what we call Tarski inverse monoids: that is, countable Boolean inverse…

Given a product X of locally compact rank one Hadamard spaces, we study asymptotic properties of certain discrete isometry groups. First we give a detailed description of the structure of the geometric limit set and relate it to the limit…

For a countable group $G$ we construct a small, idempotent complete, symmetric monoidal, stable $\infty$-category $\mathrm{KK}^{G}_{\mathrm{sep}}$ whose homotopy category recovers the triangulated equivariant Kasparov category of separable…

In this paper, I introduce weak representations of a Lie groupoid $G$. I also show that there is an equivalence of categories between the categories of 2-term representations up to homotopy and weak representations of $G$. Furthermore, I…

Let $G$ be an amenable discrete countable infinite group, $A$ a finite set, and $(\mu_g)_{g\in G}$ a family of probability measures on $A$ such that $\inf_{g\in G}\min_{a\in A}\mu_g(a)>0$. It is shown (among other results) that if the…

We introduce an equivariant version of the Cuntz semigroup, that takes an action of a compact group into account. The equivariant Cuntz semigroup is naturally a semimodule over the representation semiring of the given group. Moreover, this…

Weak unipotence of primitive ideals is a crucial property in the study of unitary representations of reductive groups. We establish a sufficient condition, referred to as mild unipotence, which guarantees weak unipotence and is more…

Let $(X,J) $ be an almost complex manifold with a (smooth) involution $\sigma:X\to X$ such that $Fix(\sigma)\neq \emptyset$. Assume that $\sigma$ is a complex conjugation, i.e, the differential of $\sigma$ anti-commutes with $J$. The space…

Let $A$ be a finite set and $G$ a group. A closed subset $X$ of $A^G$ is called a subshift if the action of $G$ on $A^G$ preserves $X$. If $K$ is a closed subset of $A^G$ such that membership in $K$ is determined by looking at a fixed…

We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault-Deaconu groupoid on our fractafold bundle and that the resulting action…

We introduce and study a notion of cylinder coherator similar to the notion of Grothendieck coherator which define more flexible notion of weak infinity groupoids. We show that each such cylinder coherator produces a combinatorial…

For every compact almost complex manifold (M,J) equipped with a J-preserving circle action with isolated fixed points, a simple algebraic identity involving the first Chern class is derived. This enables us to construct an algorithm to…

Fix a degree $d$ projective curve $X \subset \mathbb{P}^r$ over an algebraically closed field $K$. Let $U \subset (\mathbb{P}^r)^*$ be a dense open subvariety such that every hyperplane $H \in U$ intersects $X$ in $d$ smooth points. Varying…