Spivak normal fibration (Ex)

Revision as of 17:56, 9 February 2012

In the following exercises $<wikitex>; In the following exercises $X$ be a connected Poincaré complex of formal dimension $n$. {{beginthm|Exercise}} Let $\xi \colon E \to X$ be a spherical fibration $X$ with homotopy fibre $S^k$. Show that $E$ is a Poincaré complex of formal dimension $n + k$. {{endthm}} Here is an interesting problem we now confront {{beginthm|Problem}} Determine the Spivak normal fibration of $E$ above in terms of $\xi$ and the Spivak normal fibration of $X$. {{endthm}} Here are some hints for this problem: [[Tangent bundles of bundles (Ex)]] {{citeD|Wall1966a}} {{citeD|Chazin1975}} </wikitex> == References == {{#RefList:}} [[Category:Exercises]]X$ be a connected Poincaré complex of formal dimension $n$.

Here is an interesting problem we now confront

Here are some hints for this problem: Tangent bundles of bundles (Ex), [Wall1966a], [Chazin1975]

References