| Loop Space |
Article Index for Loop |
Website Links For Loop |
Information AboutLoop Space |
| CATEGORIES ABOUT LOOP SPACE | |
| topology | |
| homotopy theory | |
|
: That is, a particular Function Space . In Homotopy Theory ''loop space'' commonly refers to the same construction applied to Pointed Space s, i.e. continuous maps respecting Base Point s. In this setting there is a natural "concatenation operation" by which two elements of the loop space can be combined. With this operation, the loop space can be regarded as a Magma . If we consider the Quotient of the loop space with respect to the equivalence relation of pointed homotopy, then we obtain a Group , the well-known Fundamental Group . The iterated loop spaces of ''X'' are formed by applying Ω a number of times. The loop space construction is Right Adjoint to the Suspension Functor , and the version for pointed spaces to the Reduced Suspension . This accounts for much of the importance of loop spaces in Stable Homotopy Theory . SEE ALSO |
|
|