Related papers: Homotopy of state orbits

We construct the vortex Floer homology group $VHF (M,\mu;H)$ for an aspherical Hamiltonian $G$-manifold $(M, \omega)$ with moment map $\mu$ and a class of $G$-invariant Hamiltonian loop $H_t$, following the proposal of [3]. This is a…

Let $f$ be a rational map of degree $d\geq 2$. The moduli space $\mathcal{M}_f$, introduced by McMullen and Sullivan, is a complex analytic space consisting all quasiconformal conjugacy classes of $f$. For $f$ that is not flexible Latt\`es,…

A closed real subspace V of a complex Hilbert space H is called standard if V intersects iV trivially and and V + i V is dense in H. In this note we study several aspects of the geometry of the space Stand(H) of standard subspaces. In…

Inspired by the construction of the Cuntz semigroup for a C*-algebra, we introduce the matrix Malcolmson semigroup and the finitely presented module Malcolmson semigroup for a unital ring. These two semigroups are shown to have isomorphic…

In this paper we will define an invariant $mc_{\infty}(f)$ of maps $f:X \rightarrow Y_{\mathbb{Q}}$ between a finite CW-complex and a rational space $Y_{\mathbb{Q}}$. We prove that this invariant is complete, i.e.…

For any injective von Neumann algebra R and any discrete, countable group G, which acts by *-automorphisms on R, we construct an idempotent mapping of an ultra-weakly dense subspace of B(H) onto the reducerd crossed product von Neumann…

This paper introduces a canonical Polish groupoid associated to any separable unital C*-algebra, termed the unitary conjugation groupoid. It is defined as the semidirect product of the algebra's dual space by its unitary group, acting by…

We analyze properties of a map B = f(U) sending a unitary matrix U of size N into a doubly stochastic matrix defined by B_{i,j} = |U_{i,j}|^2. For any U we define its DEFECT, determined by the dimensionality of the space being the image…

We investigate inductive types in type theory, using the insights provided by homotopy type theory and univalent foundations of mathematics. We do so by introducing the new notion of a homotopy-initial algebra. This notion is defined by a…

We study the orbit behavior of a four dimensional smooth symplectic diffeomorphism $f$ near a homoclinic orbit $\Gamma$ to an 1-elliptic fixed point under some natural genericity assumptions. 1-elliptic fixed point has two real eigenvalues…

We consider the moduli space MN of flat unitary connections on an open Kaehler manifold U (complement of a divisor with normal crossings) with restrictions on their monodromy transformations. Using intersection and L2 cohomologies with…

An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework…

The paper is concerned with defining a topology on the set of ideals of codimension d of the algebra C^\infty(M,R) with M being a compact smooth manifold. Its main property is that it is compact Hausdorff and it contains as a subspace the…

Topological band theory has been studied for free fermions for decades, and one of the most profound physical results is the bulk-boundary correspondence. Recently a focus in topological physics is extending topological classification to…

Let C_n(M) be the configuration space of n distinct ordered points in M. We prove that if M is any connected orientable manifold (closed or open), the homology groups H_i(C_n(M); Q) are representation stable in the sense of [Church-Farb].…

If A is a bialgebra over a field k and M, N are either left-right Yetter-Drinfel'd modules or left-right Hopf modules over A, we construct deformation cohomologies H^*(M,N) as total cohomologies of certain double complexes Y(M,N) and…

The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular Hopf algebras. Pseudo-modular Hopf algebras are a…

Homotopy Type Theory with a univalent universe $\,\mathcal{U}_0$ is interpreted at the strength of finite order arithmetic. We eliminate Grothendieck universes, avoid the axiom of replacement, and bound all uses of separation.

Let F be a finitely generated discrete group. Given a covering map H to G of Lie groups with G either compact or complex reductive, there is an induced covering map Hom(F, H) to Hom(F, G). We show that when the fundamental group of G is…

Let $H$ be a closed subgroup of a regular abelian paratopological group $G$. The group reflexion $G^\flat$ of $G$ is the group $G$ endowed with the strongest group topology, weaker that the original topology of $G$. We show that the…