Whitehead torsion (Ex)
From Manifold Atlas
Revision as of 13:20, 29 July 2013 by Diarmuid Crowley (Talk | contribs)
Show that for the generator is a unit and hence defines an element in . Prove that we obtain a well-defined map
by sending the class represented by the -automorphism to , where is the -linear map
with respect to the -action on given by multiplication with . Finally show that generates an infinite cyclic subgroup in .
This is a detailed version of [Milnor1966, Example 6.6] and [Kreck&Lück2005, Ex 5.4].
-t-t^{-1}$ is a unit in $\Zz[\Zz/5]$. Conclue that $\text{Wh}(\Zz/5)$ contains an element of infinite order. This is {{citeD|Milnor1966|Example 6.6}} and {{citeD|Kreck&Lück2005|Ex 5.4}}. [[Category:Exercises]] [[Category:Exercises without solution]]1 - t - t^{-1} \in \Zz[\Zz/5] for the generator is a unit and hence defines an element in . Prove that we obtain a well-defined mapby sending the class represented by the -automorphism to , where is the -linear map
with respect to the -action on given by multiplication with . Finally show that generates an infinite cyclic subgroup in .
This is a detailed version of [Milnor1966, Example 6.6] and [Kreck&Lück2005, Ex 5.4].