Any endomorphism of a finitely generated free group naturally descends to an injective endomorphism of its stable quotient. In this paper, we prove a geometric incarnation of this phenomenon: namely, that every expanding irreducible train track map inducing an endomorphism of the fundamental group gives rise to an expanding irreducible train track representative of the injective endomorphism of...

For a connected reductive group G and a finite–dimensional G–module V , we study the invariant Hilbert scheme that parameterizes closed G–stable subschemes of V affording a fixed, multiplicity–finite representation of G in their coordinate ring. We construct an action on this invariant Hilbert scheme of a maximal torus T of G, together with an open T–stable subscheme admitting a good quotient. ...

A central principle of this paper is that, for a finitely presented group G, the algebraic properties of its finite index subgroups should be reflected by the geometry of its finite quotients. These quotients can indeed be viewed as geometric objects, in the following way. If we pick a finite set of generators for G, these map to a generating set for any finite quotient and hence endow this quo...

The Hunter–Saxton equation is the Euler equation for the geodesic flow on the quotient space of the infinite-dimensional group of orientation preserving diffeomorphisms of the unit circle modulo the subgroup of rigid rotations equipped with a right-invariant metric. We establish several properties of this quotient space: it has constant sectional curvature equal to 1, the Riemannian exponential...

We prove that the Reeb space of a proper definable map in an arbitrary o-minimal expansion of the reals is realizable as a proper definable quotient. We also show that the Betti numbers of the Reeb space of a map f can be arbitrarily large compared to those of X, unlike in the special case of Reeb graphs of manifolds. Nevertheless, in the special case when f : X → Y is a semi-algebraic map and ...

Let N be a closed spin manifold with positive scalar curvature and DN the Dirac operator on N. M1 M2 two Galois covers of such that is quotient M1. Then map from to naturally induces maps between geometric C⁎-algebras associated manifolds. We prove, by finite-propagation argument, maximal higher rho invariants lifts behave functorially respect above map. This can applied computation invariants,...

the concept of right (left) quotient (or residual) of an ideal η by anideal ν of an l-subring μ of a ring r is introduced. the right (left) quotients areshown to be ideals of μ . it is proved that the right quotient [η :r ν ] of an idealη by an ideal ν of an l-subring μ is the largest ideal of μ such that[η :r ν ]ν ⊆ η . most of the results pertaining to the notion of quotients(or residual) of ...

We give a new manifestly natural presentation of the supergravity c-map. achieve this by giving more explicit description correspondence between projective special Kähler manifolds and variations Hodge structure, demonstrating that twist construction Swann, for certain kind data, reduces to quotient discrete group. combine these two ideas showing structure rise aforementioned data then applying...

Let A be a essentially small abelian category and C Serre subcategory of . Consider the quotient functor q : → / For an object ∈ non-negative integer k we investigate when natural map X , i Ext ( ) is invertible for every { 0 1 ⋯ } In end give application main theorem.

The Johnson kernel is the subgroup of the mapping class group of a surface generated by Dehn twists along bounding simple closed curves, and has the second Johnson homomorphism as a free abelian quotient. We will determine the kernel of the map induced on the second rational cohomology by the second Johnson homomorphism in terms of the representation theory of the symplectic group.