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Topology of cell complexes and manifolds, classification of manifolds (e.g. smoothing, surgery), low dimensional topology (e.g. knot theory, invariants of 4-manifolds), embedding theory, combinatorial and PL topology, geometric group theory, infinite dimensional topology (e.g. Hilbert cube manifolds, theory of retracts).

21 votes
0 answers
854 views

A mysterious paper of Stallings that was supposed to appear in the Annals

In Stallings's paper Stallings, John, Groups with infinite products, Bull. Amer. Math. Soc. 68 (1962), 388–389. he briefly discusses how to prove "several generalizations" of Brown's theorem saying …
Laura's user avatar
  • 353
7 votes
1 answer
235 views

Expositions of Stallings's fibration theorem

In his famous paper Stallings, John, On fibering certain 3-manifolds. 1962 Topology of 3-manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) pp. 95–100 Prentice-Hall, Englewood C …
Laura's user avatar
  • 353
7 votes
1 answer
366 views

Two details from Stallings's proof of the sphere theorem

EDIT: After a little prompting by Mark Grant, I answered the first question in the comments. The second question remains open. Let $M$ be a compact $3$-manifold with $\pi_2(M) \neq 0$. The sphere t …
Laura's user avatar
  • 353