Factorization homology of stratified spaces
... map, one can then construct a link homology theory, via factorization homology with coefficients in this triple. This promises to provide a new source of such knot homology theories, similar to Khovanov homology. Khovanov homology itself does not fit into this structure, for a very simple reason: an ...
... map, one can then construct a link homology theory, via factorization homology with coefficients in this triple. This promises to provide a new source of such knot homology theories, similar to Khovanov homology. Khovanov homology itself does not fit into this structure, for a very simple reason: an ...
![arXiv:1205.2342v1 [math.GR] 10 May 2012 Homogeneous compact](http://s1.studyres.com/store/data/014455921_1-3cd5e27d3d632291f2fbeb8ac68a29b6-300x300.png)
arXiv:1205.2342v1 [math.GR] 10 May 2012 Homogeneous compact
... We classify compact homogeneous geometries which look locally like compact spherical buildings. Geometries which look locally like buildings arise naturally in various recognition problems in group theory. Tits’ seminal paper A local approach to buildings [51] is devoted to them. Among other things, ...
... We classify compact homogeneous geometries which look locally like compact spherical buildings. Geometries which look locally like buildings arise naturally in various recognition problems in group theory. Tits’ seminal paper A local approach to buildings [51] is devoted to them. Among other things, ...
Separated and proper morphisms
... The notions of separatedness and properness are the algebraic geometry analogues of the Hausdorff condition and compactness in topology. For varieties over the complex numbers, it is possible to use the “analytic topology” inherited from the usual topology on C in place of the Zariski topology, and ...
... The notions of separatedness and properness are the algebraic geometry analogues of the Hausdorff condition and compactness in topology. For varieties over the complex numbers, it is possible to use the “analytic topology” inherited from the usual topology on C in place of the Zariski topology, and ...
CROSSED PRODUCT STRUCTURES ASSOCIATED WITH
... dynamical system Σ is equivalent to studying the pair (C(X), α), where the integers act on C(X) via iterations of α. Given another compact Hausdorff space, Y , one can use an argument similar to the above to conclude that there exists a homeomorphism between X and Y if and only if C(X) is isomorphic ...
... dynamical system Σ is equivalent to studying the pair (C(X), α), where the integers act on C(X) via iterations of α. Given another compact Hausdorff space, Y , one can use an argument similar to the above to conclude that there exists a homeomorphism between X and Y if and only if C(X) is isomorphic ...
Metric geometry of locally compact groups
... – And the tightly interwoven developments of combinatorial group theory and low dimensional topology, from Dehn to Thurston, and so many others. From 1980 onwards, for all these reasons and under guidance of Gromov, in particular of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group commu ...
... – And the tightly interwoven developments of combinatorial group theory and low dimensional topology, from Dehn to Thurston, and so many others. From 1980 onwards, for all these reasons and under guidance of Gromov, in particular of his articles [Grom–81b, Grom–84, Grom–87, Grom–93], the group commu ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.