the mathematical field of algebraic topology, the fundamental group of a topological space is the group of the equivalence classes under homotopy of the...

The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces. In algebraic...

The Fundamental Fysiks Group was founded in San Francisco in May 1975 by two physicists, Elizabeth Rauscher and George Weissmann, at the time both graduate...

In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or...

expresses the structure of the fundamental group of a topological space X {\displaystyle X} in terms of the fundamental groups of two open, path-connected...

described as a fundamental polygon ABA−1B−1. The fundamental group of the torus is just the direct product of the fundamental group of the circle with...

rap group Fundamental (Bonnie Raitt album), 1998 Fundamental (Pet Shop Boys album), 2006 Fundamental (Puya album) or the title song, 1999 Fundamental (Mental...

than 0. It encodes not only the topology of the surface through its fundamental group but also determines the Riemann surface up to conformal equivalence...

> 2 the fundamental group of SO(n, R) is cyclic of order 2, and the spin group Spin(n) is its universal cover. For n = 2 the fundamental group is infinite...

characteristics of underlying space. In the above example, the orbifold fundamental group of O is Z 2 {\displaystyle \mathbb {Z} _{2}} and its orbifold Euler...

have the same Betti numbers but distinct fundamental groups. He posed the question of whether the fundamental group is sufficient to topologically characterize...

generalization used in algebraic geometry is the étale fundamental group. A Lie group is a group that also has the structure of a differentiable manifold;...

Fundamental rights are a group of rights that have been recognized by a high degree of protection from encroachment. These rights are specifically identified...

group cannot be free, since the elements of a free generating set of a free group have infinite order. In algebraic topology, the fundamental group of...

homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, denoted...

theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra...

Galois correspondence between covering spaces and subgroups of the fundamental group. Most “nice” spaces such as manifolds and CW complexes are semi-locally...

atom, and three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation...

In physics, the fundamental interactions or fundamental forces are the interactions that do not appear to be reducible to more basic interactions. There...

is contractible, the fundamental group of GL+(n, R) is isomorphic to that of SO(n). The homeomorphism also shows that the group GL(n, R) is noncompact...

universal cover, whose center is the fundamental group of the simple Lie group. The corresponding simple Lie groups with non-trivial center can be obtained...

orbifold fundamental group of B (which is not the same as the fundamental group of the underlying topological manifold). The image of group π 1 ( S 1...

trivial), so SO(n) is connected and has fundamental group Z2 while PSO(n) is connected and has fundamental group equal to the center of Spin(n). In indefinite...

group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler...

theory, an algebraic definition of fundamental groups of schemes giving birth to the now famous étale fundamental group and he then conjectured the existence...

such a hole cannot be continuously transformed into each other. The fundamental group of a topological space is an indicator of the failure for the space...

tool in the calculation of homotopy groups. A standard example in this vein is the calculation of the fundamental group of the circle by means of the covering...

topology, defining braid groups as fundamental groups of a configuration space. Alternatively, one can define the braid group purely algebraically via...

considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and maps between these algebraic...

modern usage allows any discrete subgroup. When Γ is isomorphic to the fundamental group π 1 {\displaystyle \pi _{1}} of a hyperbolic 3-manifold, then the...