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...le. It was difficult to find appropriate references. The proofs are really elementary, but use ideas that are barely applicable in similar high-dimensional situa The following elementary facts hold for $n$-manifolds of any dimension $n$:

... imply the claim appearing in Theorem \ref{the:status_of-Farrell-Jones} by surgery theory. ...o not get information in dimensions $n \le 4$ for the usual problems about surgery. In the case $n = 3$ there is the conjecture of Cannon <nowiki>[</nowiki>[[

==Functoriality and elementary examples== ...plicial volume of the torus is zero ([[Simplicial volume#Functoriality and elementary properties|see above]]), but the simplicial volume of an oriented closed co

...nifolds. This is not the place to describe this method, which is called '''surgery theory'''. But the following can be said. The most successful way to decide ...ove it until it is an $h$-cobordism. They solve this problem completely by surgery theory.

...e used during the [[:Category:Oberwolfach Surgery Seminar 2012|Oberwolfach Surgery Seminar 2012]]. It is intended as a reference guide for reading before the * [[Oberwolfach Surgery Seminar 2012: Discussion|Discussion]]

* [[Regensburg Surgery Blockseminar 2012: General information|General information]] * [[Regensburg Surgery Blockseminar 2012: Program|Program]]

... of $M \sharp N$ is well-defined: in fact $M \sharp N$ is the outcome of 0-surgery on $M \sqcup N$. The essential point is \cite{Hirsch} which states, for an ...quivalent: the first has signature 2 the other signature 0. The following elementary lemma is often useful to remember.

== Surgery: high-d methods in low-d== === Lecture 1: Normal maps and the surgery obstruction===