space and p : E → B {\displaystyle p\colon E\to B} is any covering map, then E is aspherical if and only if B is aspherical.) Each aspherical space X...

Aspherical may refer to: Aspherical space, a concept in topology Aspherical lens, a type of lens assembly used in photography which contains an aspheric...

superperfect (hence perfect) but not acyclic. Aspherical space Dror, Emmanuel (1972), "Acyclic spaces", Topology, 11 (4): 339–348, doi:10.1016/0040-9383(72)90030-4...

sequence in a graded algebra finitely generated over a field. Let X be an aspherical space, i.e., its universal cover E is contractible. Then every singular (or...

interpretation. It is known that H {\displaystyle \mathbb {H} } is an aspherical space, i.e. all higher homotopy and homology groups of H {\displaystyle \mathbb...

Eilenberg–MacLane space is a topological space with a single nontrivial homotopy group. Let G be a group and n a positive integer. A connected topological space X is...

fibration is a proper approximate fibration between manifolds. aspherical space Aspherical space assembly map Atiyah 1.  Michael Atiyah. 2.  Atiyah duality...

spaces, such as tori, all higher homotopy groups (that is, second and higher homotopy groups) are trivial. These are the so-called aspherical spaces....

determined up to isomorphism by their fundamental group. The total spaces are aspherical (in other words all higher homotopy groups vanish). They have Thurston...

galactic dark-matter haloes was titled "Milking the spherical cow – on aspherical dynamics in spherical coordinates". References to the joke appear even...

optical components are an easy-to-make spherical primary mirror, and an aspherical correcting lens, known as a Schmidt corrector plate, located at the center...

{\displaystyle t_{x}\colon T_{X}\to X} where T X {\displaystyle T_{X}} is an aspherical space. Furthermore, the induced map π 1 ( T X ) → π 1 ( X ) {\displaystyle...

Aileen Wu as six downtrodden young space colonists who encounter hostile creatures while scavenging a derelict space station in which they plan to navigate...

mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible...

components are extreme aspherical elements for chromatic aberration reduction and better resolution results, three aspherical elements, two extra-low...

homeomorphism. Since aspherical manifolds with isomorphic fundamental groups are homotopy equivalent, the Borel conjecture implies that aspherical closed manifolds...

{\displaystyle {\mathcal {H}}(K)} is always aspherical, regardless of whether K {\displaystyle K} is aspherical. Moreover, despite the name of the procedure...

well as whether a best spherical form of lens or an optically optimal aspherical form was used in the manufacture of the lens. Generally, the best spherical...

in 2005. Ontaneda's work deals with the geometry and topology of aspherical spaces, with particular attention to the relationship between exotic structures...

Proposition 11.1, p. 161 Dyer, Eldon; Vasquez, A. T. (1973). "Some small aspherical spaces". Journal of the Australian Mathematical Society. 16 (3): 332–352...

important effect, because spherical shapes are much easier to produce than aspherical ones. In many cases, it is cheaper to use multiple spherical elements...

{\displaystyle 3\leq \operatorname {cd} (G)\leq n} ), one can construct an aspherical CW complex X of dimension n whose fundamental group is G. The theorem...

solvmanifold is aspherical. Among all compact homogeneous spaces, solvmanifolds may be characterized by the properties of being aspherical and having a solvable...

al. argued in 2019 that HE 1327−2326's metal enrichment was due to an aspherical supernova explosion of a 25 M☉ Population III star which enriched the...

Maillot, S.; Porti, J. (2007). "Weak collapsing and geometrization of aspherical 3-manifolds". arXiv:0706.2065 [math.GT]. Bessieres, L.; Besson, G.; Boileau...

Eilenberg–MacLane space of the finite cyclic group of order 2. All compact aspherical manifolds are essential (since being aspherical means the manifold...

demonstrates that a non-positively curved polyhedral cell complex is aspherical. This fact is of crucial importance for modern geometric group theory...

wide-angle lenses: 43 mm f/4.5. prototype lens. ULD glass, floating system and aspherical. 21 mm equivalent 50 mm f/4.5. Two versions exist, the non ULD and ULD...

viewfinder, with three mirrors (including one Fresnel reflector) of unusual, aspheric shapes set at odd angles to create an erect image on the film and an erect...

sign conjecture but which does not refer to Riemannian geometry at all. Aspherical manifolds are connected manifolds for which all higher homotopy groups...