Hermit crab wood and stone are used by some species). The tip of the hermit crab's abdomen is adapted to clasp strongly onto the columella of the snail shell. Most hermit crabs are nocturnal. Hermit crabs can be divided into two groups: As hermit crabs grow, they require larger shells. Since suitable intact gastropod shells are sometimes a limited resource, vigorous competition often occurs among hermit crabs for shells. The availability of empty shells at any given place depends on the relative abundance of gastropods and hermit crabs, matched for size. An equally important issue is the population of organisms that prey
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