cubically thin homotopy
0.1 Cubically thin homotopy
Let u,u′ be squares in X with common vertices.
-
1.
A cubically thin homotopy U:u≡□Tu′ between u and u′ is a cube (http://planetmath.org/Polyhedron) U∈R□3(X) such that
-
2.
The square u is cubically T-equivalent
to u′, denoted u≡□Tu′ if there is a cubically thin homotopy between u and u′.
This definition enables one to construct the homotopy double groupoid scheme 𝝆□2(X) , by defining a
relation
of cubically thin homotopy on the set R□2(X) of squares.
References
-
1
K.A. Hardie, K.H. Kamps and R.W. Kieboom, A homotopy 2-groupoid of a Hausdorff space,
Applied Cat. Structures
, 8 (2000): 209-234.
- 2 R. Brown, K.A. Hardie, K.H. Kamps and T. Porter, A homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories 10,(2002): 71-93.
Title | cubically thin homotopy |
Canonical name | CubicallyThinHomotopy |
Date of creation | 2013-03-22 18:15:06 |
Last modified on | 2013-03-22 18:15:06 |
Owner | bci1 (20947) |
Last modified by | bci1 (20947) |
Numerical id | 17 |
Author | bci1 (20947) |
Entry type | Definition |
Classification | msc 55N33 |
Classification | msc 55N20 |
Classification | msc 55U40 |
Classification | msc 18D05 |
Synonym | higher dimensional thin homotopy |
Related topic | HomotopyDoubleGroupoidOfAHausdorffSpace |
Related topic | HomotopyAdditionLemma |
Related topic | WeakHomotopyAdditionLemma |
Related topic | Polyhedron |
Defines | higher dimensional thin Homotopy |