space fibration. The path space fibration can be understood to be dual to the mapping cone.[clarification needed] The fiber of the based fibration is called...

following commutative diagram shows the situation: : 66  A fibration (also called Hurewicz fibration) is a mapping p : E → B {\displaystyle p\colon E\to B}...

Moore's path space, see path space fibration#Moore's path space. See also: loop space, the space of loops in a topological space This disambiguation page...

example of a G-fibration. Another example is Moore's path space fibration: namely, let P ′ X {\displaystyle P'X} be the space of paths of various length...

{\displaystyle PX\to X,\,\chi \to \chi (1)} is a fibration called the path space fibration. mapping space Martin Frankland, Math 527 - Homotopy Theory -...

→ B {\displaystyle f\colon X\to B} be a Serre fibration of topological spaces, and let F be the (path-connected) fiber. The Serre cohomology spectral...

universal fibration was univalent: the associated fibration of pairwise homotopy equivalences between the fibers is equivalent to the paths-space fibration of...

a fibration, then the homotopy fiber is simply the fiber of the replacement fibration. We recall this construction of replacing a map by a fibration: Given...

MacPherson. G-fibration A G-fibration with some topological monoid G. An example is Moore's path space fibration. G-space A G-space is a space together with...

X {\displaystyle p:E\to X} is a fibration, because a Hurewicz fibration can be checked locally on a paracompact space. While a cofibration is injective...

speaking, it is a continuous map p: E → B having the same behaviour as a fibration regarding the (relative) homotopy groups of E, B and p−1(x). Equivalently...

Example: the Hopf fibration. Let B equal S 2 {\displaystyle S^{2}} and E equal S 3 . {\displaystyle S^{3}.} Let p be the Hopf fibration, which has fiber...

20 cell rings is one of 5 fibrations within the fibration of 12 of 72 decagons: a fibration of a fibration. All the fibrations have this two level structure...

\pi } has the homotopy lifting property. A weaker notion of fibration is Serre fibration, for which homotopy lifting is only required for all CW complexes...

fibration for details of the projectivization construction in this case. The Cartesian product of projective Hilbert spaces is not a projective space...

needed a spectral sequence in homology that applied to path space fibrations, whose total spaces are almost never locally compact, thus was unable to use...

hexagonal fibration. They intersect the other three, which belong to another hexagonal fibration. The three parallel great circles of each fibration spiral...

covering groups. Fibrations provide a very powerful means to compute homotopy groups. A fibration f the so-called total space, and the base space B has, in particular...

International Space Station (ISS) is a large space station that was assembled and is maintained in low Earth orbit by a collaboration of five space agencies...

category D(A). In any model category, a fibration that is also a weak equivalence is called a trivial (or acyclic) fibration. A cofibration that is also a weak...

special case of a fibration, and use the homotopy lifting property to "follow" paths on the base space X {\displaystyle X} (we assume it path-connected for...

subject to the following axioms. A fibration that is also a weak equivalence is called an acyclic (or trivial) fibration and a cofibration that is also a...

sequence of a fibration that higher homotopy groups of a space and its universal cover are same. (By the same argument, if E is a path-connected space and p :...

precisely, twistor space is T := C 4 . {\displaystyle \mathbb {T} :=\mathbb {C} ^{4}.} It has associated to it the double fibration of flag manifolds P...

_{i}(S^{15})\oplus \pi _{i-1}(S^{7}).} The three fibrations have base space Sn with n = 2m, for m = 1, 2, 3. A fibration does exist for S1 (m = 0) as mentioned...

of many turns of optical fibre. The strength of the Sagnac effect is dependent on the effective area of the closed optical path: this is not simply the...

Canonical line bundle Vector bundle Associated bundle Fibration Hopf bundle Classifying space Cofibration Homotopy groups of spheres Plus construction...

path in space does not follow that of the light signals, for example in the standard rotating platform case (FOG) but with a non-circular light path....

generally, for fibrations with certain conditions. If p : E → B {\displaystyle p\colon E\to B} is a fibration with fiber F, with the base B path-connected...

trivial. Recall there is a spectral sequence for any Serre fibration, such as the fibration K ( π n + 1 ( X ) , n + 1 ) ≃ F n + 1 → S n + 1 n → S n n ≃...