Difference between revisions of "Simple homotopy type"
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+ | Two CW-complexes $ K $, | ||
+ | $ L $ | ||
+ | are simple homotopy equivalent if there is a homotopy equivalence $ \tau : K \rightarrow L $ | ||
+ | whose [[Whitehead torsion|Whitehead torsion]] vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type. | ||
====Comments==== | ====Comments==== | ||
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====References==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> G. de Rham, "Torsion et type simple d'homotopie" , ''Lect. notes in math.'' , '''48''' , Springer (1967)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> G. de Rham, "Torsion et type simple d'homotopie" , ''Lect. notes in math.'' , '''48''' , Springer (1967)</TD></TR></table> |
Latest revision as of 08:13, 6 June 2020
Two CW-complexes $ K $,
$ L $
are simple homotopy equivalent if there is a homotopy equivalence $ \tau : K \rightarrow L $
whose Whitehead torsion vanishes. An equivalence class under simple homotopy equivalence is called a simple homotopy type.
Comments
References
[a1] | G. de Rham, "Torsion et type simple d'homotopie" , Lect. notes in math. , 48 , Springer (1967) |
How to Cite This Entry:
Simple homotopy type. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_homotopy_type&oldid=48705
Simple homotopy type. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Simple_homotopy_type&oldid=48705