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There are a lot of books dealing with the strangeness of the topology of 4-dimensional topology. I wonder if there are books or overview references on the topology of n-manifolds (where n > 4) ?

Reading through Scorpan's "The wild word of 4-manifolds", you can read (in short notices) about these subject (for example the use of $\pi_i(PL/DIFF)$ etc, exotic structures on higher dimensional manifolds and so on). What is the standard reference on these subjects ?

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up vote 5 down vote accepted

Kosinski's "Differentiable Manifolds" and Milnor's h-cobordism theorem lecture notes I consider to be two of the standard high-dimensional manifold theory textbooks.

  • Kosinski, Differential Manifolds, Volume 138 (Pure and Applied Mathematics)

  • Milnor, John, Lectures on the h-cobordism theorem, notes by L. Siebenmann and J. Sondow, Princeton University Press, Princeton, NJ, 1965. v+116 pp.

another popular reference in the PL case is:

  • Rourke, Colin Patrick; Sanderson, Brian Joseph, Introduction to piecewise-linear topology, Springer Study Edition, Springer-Verlag, Berlin-New York, 1982. ISBN 3-540-11102-6.

I believe they go as far as the $s$-cobordism theorem in that reference but I don't have a copy.

The standard references for the relationship between topological, smooth and PL structures would be Kirby and Siebenmann:

  • Kirby, Robion C.; Siebenmann, Laurence C. (1977) Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. Princeton, NJ: Princeton Univ. Pr.. ISBN 0-691-08191-3

of all the above references I find this one the least reader-friendly, as it tends to be more heavy on technical constructions and steers-away from narrative. The above is still missing a lot of details -- for much of this material people still go back to Milnor's papers rather than book references. Milnor's writing is quite pleasant, for example you'll have to go there for his work on microbundles.

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Thanks, I forgot about the copy of Kosinski (it was hiding in a book closet). For Milnor I have to go to the University library I guess... – Willem Noorduin Jul 24 '11 at 15:20
For Milnor's h-cobordism notes I suggest you do a Google search. It's been out of print for some time and is otherwise hard to find. – Ryan Budney Jul 24 '11 at 16:46
Seems like they are reprinting "The collected Papers of Milnor" (for example…). I don't know in which volume it is in,... – Willem Noorduin Jul 25 '11 at 7:38
I don't think it's in any volume. The collected works consists of his papers, not his books. – Ryan Budney Jul 25 '11 at 16:29

Wall's Surgery on Compact Manifolds is a classic, and it's very good.

Ranicki's Algebraic and Geometric Surgery is also tremendously good.

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