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<?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"><wikitex>; {{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}} </wikitex> == 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&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>