Loggerhead sea turtle turtle is debated, but most authors consider it a single polymorphic species. Molecular genetics has confirmed hybridization of the loggerhead sea turtle with the Kemp's ridley sea turtle, hawksbill sea turtle, and green sea turtles. The extent of natural hybridization is not yet determined; however, second-generation hybrids have been reported, suggesting some hybrids are fertile. Although evidence is lacking, modern sea turtles probably descended from a single common ancestor during the Cretaceous period. Like all other sea turtles except the leatherback, loggerheads are members of the ancient family Cheloniidae, and appeared about 40 million years ago. Of the six species
History of manifolds and varieties History of manifolds and varieties The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology. Certain special classes of manifolds also have additional algebraic structure; they may behave like groups, for instance. In that case, they are called Lie Groups. Alternatively, they may be described by polynomial equations, in which case they are called algebraic varieties, and if they additionally carry a group structure, they are called algebraic groups. The term "manifold" comes from German "Mannigfaltigkeit," by Riemann. In English, "manifold" refers to