Fiddler crab a vital role in the preservation of wetland environments; by sifting through the sands, they aerate the substrate and prevent anaerobic conditions. Fiddler crabs live rather brief lives of no more than two years (up to three years in captivity). Male fiddler crabs use the major claw to perform a waving display as a form of female courtship. Females choose their mate based on claw size and also quality of the waving display. In many fiddler crab species, the female occupies the burrow of their mate while she lays her clutch of eggs. Research shows that the male major claw
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