<?xml version="1.0"?>
<api>
  <query-continue>
    <allpages gapfrom="Regensburg Surgery Blockseminar 2012: General information" />
  </query-continue>
  <query>
    <pages>
      <page pageid="1551" ns="0" title="Reducible Poincaré Complexes (Ex)">
        <revisions>
          <rev xml:space="preserve">&lt;wikitex&gt;;
{{beginthm|Exercise}}
Let $X$ be a finite Poinaré complex of formal dimension $n \geq 3$ with Spivak Normal Fibration $\nu_X$. A theorem of Wall, \cite{Wall1967a|Theorem 2.4}, states that $X$ may be written
$$ X \simeq X^\bullet \cup_\phi e^n$$
where $X^\bullet$ has dimension less than $n$.  Show that for some $k$, the top cell of $X$ splits off, i.e. $\Sigma^k X \simeq S^{n+k} \vee \Sigma^k X^\bullet$, if and only if $\nu_X$, the Spivak normal fibration of $X$, is trivial.
{{endthm}}
&lt;/wikitex&gt;
== References ==
{{#RefList:}}
[[Category:Exercises]]
[[Category:Exercises without solution]]</rev>
        </revisions>
      </page>
      <page pageid="1349" ns="0" title="Regensburg Surgery Blockseminar 2012: Exercises">
        <revisions>
          <rev xml:space="preserve">This page lists the exercises for consideration during the Blockseminar.  Participants are encouraged submit exercises related to their own talks and to work on solutions to all exercises.

* [[Regensburg Surgery Blockseminar 2012: General information|General information]]
* [[Regensburg Surgery Blockseminar 2012: Program|Program]]
* [[:Category:Surgery|Surgery on the Manifold Atlas]] 

==[A] Talks 1-3== 
*[[Handlebody decompositions of bordisms (Ex)]]
*[[Elementary matricies (Ex)]]
*[[Whitehead torsion (Ex)]]
*[[Whitehead torsion II (Ex)]]
*[[Whitehead torsion III (Ex)]]
*[[Whitehead torsion IV (Ex)]]
*[[Whitehead torsion V (Ex)]]

==[B] Talks 4&amp;5==
*[[Poincaré duality (Ex)]]
*[[Poincaré duality II (Ex)]]
*[[Poincaré duality III (Ex)]]
*[[Poincaré duality IV (Ex)]]
*[[Spivak normal fibration (Ex)]]
==[C] Talks 6-8==
*[[Bundle structures and lifting problems (Ex)]]
*[[Normal bordism - definitions (Ex)]]
*[[Thom spaces (Ex)]]
*[[Cell attachments for surgery (Ex)]]
*[[Regular homotopy group of immersions (Ex)]]
*[[Normal maps and submanifolds (Ex)]]
*[[Immersing n-spheres in 2n-space (Ex)]]
*[[Sphere bundles and spin (Ex)]]

==[D] Talks 9-11==
*[[Homology braid II (Ex)]]
*[[Heegaard splittings (Ex)]]
*[[Kernel formation (Ex)]]
*[[Middle-dimensional surgery kernel (Ex)]]
*[[Even dimensional surgery obstruction (Ex)]]
*[[Presentations (Ex)]]
*[[Quadratic formations (Ex)]]

==[E] Talks 12-14==
* [[Plumbing (Ex)]]
* [[Wall realisation (Ex)]]

==[F] Talks 15-18==
*[[Almost framed bordism (Ex)]]
*[[Exotic spheres and chirality (Ex)]]
*[[K-invariant for G/PL (Ex)]]
*[[Splitting invariants (Ex)]]
*[[Fake projective spaces in dim 6 (Ex)]]
[[Category:Regensburg Surgery Blockseminar 2012]]</rev>
        </revisions>
      </page>
    </pages>
  </query>
</api>