Some Examples in Topology

On Some Examples in Symplectic Topology

Article is devoted to the Examples 2 and 3 of the symplectic solvable Lie groups R with some special cohomological properties, which have been constructed by Benson and Gordon. But they are not succeeded in constructing corresponding compact forms for symplectic structures on these Lie groups. Recently A.Tralle proved that there is no compact form in the Example 3. But his proof is rather compl...

Some problems in topology

Broadly speaking, we may say that analysis situs, or topology, deals with the properties of geometrical figures that remain invariant when the figures are subjected to arbitrary continuous transformations. There are, however, several distinct kinds of analysis situs, because there are several distinct ways of interpreting the physical notion of continuity in mathematical language. For example, ...

Some Examples in Toric Geometry

We present two examples in toric geometry concerning the relationship between smooth toric varieties and quasitoric manifolds (or more generally unitary torus manifolds), and extend the results of [8] to prove the non-existence of almost complex quasitorics over the duals of some certain cyclic 4-polytopes. We also provide the sufficient conditions on the base polytope and the characteristic ma...

Representations : Some Examples

Some Effective Oop Examples

This paper will present two examples that we feel can convince students of the benefits of object-oriented design and spur their interest. Both examples are well-known and fun to program. We first describe a sorting animation. In this project we will ask students to implement animation of various sorting algorithms, and for each sorting algorithm the user can choose one of two methods of animat...