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Results tagged with reference-request
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user 23571
This tag is used if a reference is needed in a paper or textbook on a specific result.
28
votes
Accepted
Unique smooth structure on 3-manifolds
An alternative to Moise's paper for the existence and uniqueness of piecewise linear (PL) structures on topological 3-manifolds is the paper "The triangulation of 3-manifolds" by A.J.S. Hamilton in Qu …
- 20k
11
votes
Diffeomorphism group of the projective plane
It is a theorem of A. Gramain from 1973 (Annales Sci. E.N.S.) that the diffeomorphism group of the projective plane has the homotopy type of $SO(3)$, the subgroup of isometries of the standard constan …
- 20k
13
votes
Accepted
Where was it first shown that every homotopy self-equivalence of $S^1\times S^2$ is homotopi...
My guess is that the oldest reference might be Pontryagin's 1941 paper on the homotopy classification of maps from a 3-dimensional complex to the 2-sphere, the English version of which is in Recueil M …
- 20k
51
votes
Accepted
Triangulating surfaces
[Three years later …]
All the published proofs of triangulability of surfaces that I am aware of use the Schoenflies theorem, which is not exactly an easy thing to prove. There is however another line …
- 20k
6
votes
Accepted
Essential surfaces in the Exterior of Montesinos knots
Most Montesinos knots and links have closed incompressible surfaces in their complements. This was shown by Ulrich Oertel in the paper "Closed incompressible surfaces in complements of star links", Pa …
- 20k
24
votes
Reference for a fact (?) on homeomorphic knot complements
This is a question that I remember worrying about when I first started learning about knot theory. Older books have a tendency to skim over this point rather lightly, perhaps because the resolution of …
- 20k
24
votes
Accepted
Points on a sphere
Let me just elaborate a little on the references that Charlie Frohman listed (so this isn't really a separate answer, but it's too long for a comment).
The theorem for equilateral triangles is due to …
- 20k
32
votes
Accepted
Survey articles on homotopy groups of spheres
While my Algebraic Topology book and my unfinished book on spectral sequences (referred to in other answers to this question) contain some information about homotopy groups of spheres, they don't real …
- 20k
22
votes
CW-structures and Morse functions: a reference request
The result you are looking for is Theorem 4.18 in "An Introduction to Morse Theory" by Yukio Matsumoto, published by AMS in 2002 (translated from Japanese). The connections between Morse functions, ha …
- 20k
82
votes
Learning Topology
Since the discussion has broadened from the original question to include a wider range of topology books, let me add one more. This is an algebraic topology book by Tammo tom Dieck published just a ye …
- 20k