Talk:Whitehead torsion II (Ex)
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Using the product formula $\tau(f \times f') = \chi(X') \left( i_* \left(\tau(f)\right)\right) + \chi(X) \left({i'}_*\left( \tau(f') \right)\right)$, where $f:X \rightarrow Y, f': X' \rightarrow Y'$ are homotopy equivalences and $i: Y \rightarrow Y \times Y', i': Y' \rightarrow Y \times Y'$ are induced by choosing basepoints, this is trivial since $\chi(S^1) = 0, \tau(\id_{S^1}) = 0$. | Using the product formula $\tau(f \times f') = \chi(X') \left( i_* \left(\tau(f)\right)\right) + \chi(X) \left({i'}_*\left( \tau(f') \right)\right)$, where $f:X \rightarrow Y, f': X' \rightarrow Y'$ are homotopy equivalences and $i: Y \rightarrow Y \times Y', i': Y' \rightarrow Y \times Y'$ are induced by choosing basepoints, this is trivial since $\chi(S^1) = 0, \tau(\id_{S^1}) = 0$. | ||
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[[Category:Exercises with solution]] | [[Category:Exercises with solution]] | ||
Revision as of 15:03, 1 April 2012
Using the product formula 
, where 
are homotopy equivalences and 
are induced by choosing basepoints, this is trivial since 
.
