We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

I am a geometric group theorist. Geometric group theory is a highly interdisciplinary field focusing on the study of groups via their actions on geometric spaces. Geometric group theory uses the tools and approaches of algebraic topology, commutative algebra, semigroup theory, hyperbolic geometry, geometric analysis, combinatorics, computational group theory, computational complexity theory, lo...

We construct rational maps from M5,1 and M6,1 to lower-dimensional moduli spaces. As a consequence, we identify geometric divisors that generate extremal rays of the effective cones for these spaces.

These notes cover the basics of Riemannian geometry, Lie groups, and symmetric spaces. This is just a listing of the basic definitions and theorems with no in-depth discussion or proofs. Some exercises are included at the end of each section to give you something to think about. See the references cited within for more complete coverage of these topics. Many geometric entities are representable...

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

We construct geometric models for cluster algebras associated with bordered surfaces with marked points, for any choice of coefficients of geometric type, using generalized decorated Teichmüller spaces. In this context, the cluster variables are interpreted as suitably renormalized lambda lengths.

14. Diagrams of spaces 68 14.1. The geometric realization and total singular complex functors 68 14.2. Filtered diagrams of simplicial sets 70 14.3. Commuting hocolim and holim: simplicial sets 72 14.4. Commuting hocolim and holim: topological spaces 74 References 75

3 Convex functions on symmetric spaces 11 3.1 Geometric preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Metric spaces with curvature bounds . . . . . . . . . . . . . . 11 3.1.2 Hadamard spaces . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Symmetric spaces of noncompact type . . . . . . . . . . . . . 15 3.1.4 Auxiliary results . . . . . . . . . . . . . . . ....

We derive Banach-Stone theorems for spaces of homogeneous polynomials. We show that every isometric isomorphism between the spaces of n-homogeneous approximable polynomials on real Banach spaces E and F is induced by an isometric isomorphism of E′ onto F ′. With an additional geometric condition we obtain the analogous result in the complex case. Isometries between spaces of n-homogeneous integ...