Related papers: A note on adjunction spaces and G-ANE's

This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.

We show that if G is a discrete subgroup of the group of the isometries of the hyperbolic k-space H^k, and if R is a representation of G into the group of the isometries of H^n, then any R-equivariant map F from H^k to H^n extends to the…

Let G be a compact group acting on a Banach space L by means of linear isometries. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact convex subsets of L endowed with the Hausdorff metric…

The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…

For discrete groups G, we introduce equivariant Nielsen invariants. They are equivariant analogs of the Nielsen number and give lower bounds for the number of fixed point orbits in the G-homotopy class of an equivariant endomorphism f:X->X.…

We prove a conjecture of B. Gr\"unbaum stating that the set of affine invariant points of a convex body equals to the set of points invariant under all affine linear symmetries of the convex body. As a consequence we give a short proof on…

We study invariant and bi-invariant metrics on groups focusing on finite groups $G$. We show that non-equivalent (bi) invariant metrics on $G$ are in 1-1 correspondence with unitary symmetric (conjugate) partitions on $G$. To every metric…

Three themes of general topology: quotient spaces; absolute retracts; and inverse limits - are reapproached here in the setting of metrizable uniform spaces, with an eye to applications in geometric and algebraic topology. The results…

We give a $K$-theoretic and geometric interpretation for a generalized weighted Ehrhart theory of a full-dimensional lattice polytope $P$, depending on a given homogeneous polynomial function $\varphi$ on $P$, and with Laurent polynomial…

We study the existence of projectable $G$-invariant Einstein metrics on the total space of $G$-equivariant fibrations $M=G/L\to G/K$, for a compact connected semisimple Lie group $G$. We obtain necessary conditions for the existence of such…

We cast Kasparov's equivariant KK-theory in the framework of model categories. We obtain a stable model structure on a certain category of locally multiplicative convex $G$-$C^*$-algebras, which naturally contains the stable…

An orbifold version of the Hitchin-Thorpe inequality is used to prove that certain weighted projective spaces do not admit orbifold Einstein metrics. Also, several estimates for the orbifold Yamabe invariants of weighted projective spaces…

We study relative algebraic K-theory of admissible Zariski-Riemann spaces and prove that it is equivalent to G-theory and satisfies homotopy invariance. Moreover, we provide an example of a non-noetherian abelian category whose negative…

A classification theorem for RK-manifolds with linear dependence between invariants of an antiholomorphic plane in the tangent space is proved.

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

We prove an equivariant analogue of Grothendieck's theorem for vector bundles on the one dimensional projective space over complex numbers.

We introduce an equivariant algebraic kk-theory for G-algebras and G-graded algebras. We study some adjointness theorems related with crossed product, trivial action, induction and restriction. In particular we obtain an algebraic version…

We develop an analog to the ends of a metric space for the category of coarse metric spaces and show that it is equivalent to a previously defined coarse invariant.

In this article we have studied bicomplex valued measurable functions on an arbitrary measurable space. We have established the bicomplex version of Lebesgue's dominated convergence theorem and some other results related to this theorem.…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…