Properties
Homotopy invariance: Let ƒ, g: X → Y be homotopy equivalences of finite connected CW-complexes. If ƒ and g are homotopic then τ(ƒ) = τ(g).
Topological invariance: If ƒ: X → Y is a homeomorphism of finite connected CW-complexes then τ(ƒ) = 0.
Composition formula: Let ƒ: X → Y, g: Y → Z be homotopy equivalences of finite connected CW-complexes. Then .
Read more about this topic: Whitehead Torsion
Famous quotes containing the word properties:
“A drop of water has the properties of the sea, but cannot exhibit a storm. There is beauty of a concert, as well as of a flute; strength of a host, as well as of a hero.”
—Ralph Waldo Emerson (1803–1882)
“The reason why men enter into society, is the preservation of their property; and the end why they choose and authorize a legislative, is, that there may be laws made, and rules set, as guards and fences to the properties of all the members of the society: to limit the power, and moderate the dominion, of every part and member of the society.”
—John Locke (1632–1704)