bio  website  math.cornell.edu/~hatcher 

location  Cornell University  
age  
visits  member for  4 years, 9 months 
seen  11 hours ago  
stats  profile views  1,880 
2d

awarded  Good Answer 
Aug 21 
answered  In a fibration, can a deformation retraction of the base be lifted to the total space? 
Aug 18 
answered  A query about Hatcher flow on arc complex 
Aug 17 
awarded  Good Answer 
Aug 14 
awarded  Nice Answer 
May 17 
revised 
Intuition behind Thom class
corrected a typo in a formula 
Feb 19 
awarded  Enlightened 
Feb 19 
comment 
Seifert fiberable manifolds with several Seifert fiberings
@Werner Thumann: That is correct, each prism manifold has exactly two Seifert fiberings. This is an interesting contrast to lens spaces, $S^3$, and $S^1\times S^2$, each of which has infinitely many different Seifert fiberings. 
Feb 18 
awarded  Nice Answer 
Feb 16 
revised 
Seifert fiberable manifolds with several Seifert fiberings
added 45 characters in body 
Feb 16 
answered  Seifert fiberable manifolds with several Seifert fiberings 
Feb 1 
comment 
Adams' theorems on the HopfWhitehead Jhomomorphism
For question 1, I think there is a similar sort of argument to show injectivity in these cases, though it needs a bit more input, notably Adams operations in real Ktheory. I have some handwritten notes on this from 20 years ago that would take some work to decipher after this long a time. My recollection is that I extracted these from Adams' J(X)  IV paper. My plan was, and still is, to include this in that unfinished book mentioned in the question, though as the years pass the chances of this ever happening become increasingly slim. 
Jan 21 
comment 
Foliation of surface all of whose leaves are circles
One can also reduce the case of nonempty boundary to the closed case by doubling: Take two copies of the surface with boundary and identify their boundaries to get a closed surface. If you know the closed surface is a torus, the original surface must then be an annulus. (Doubling doubles the Euler characteristic.) 
Jan 20 
answered  Moore decomposition, dual to Postnikov tower 
Dec 26 
answered  Action of Mapping Class Group on Arc complex 
Dec 16 
comment 
Codimension zero embeddings and diffeomorphism groups
The paper of LaBach mentioned in an earlier comment (now deleted?) uses a nonstandard topology on $Diff(D^n)$. The restriction map $Diff(D^n)\to Diff(int(D^n))$ is injective so can be viewed as an inclusion, and LaBach uses the subspace topology on $Diff(D^n)$ induced from the compactopen topology on $Diff(int(D^n))$. In this topology one can do a sort of "reverse Alexander trick" and push all the complications of a diffeomorphism of $D^n$ out to $\partial D^n$ and make them disappear. 
Dec 16 
comment 
Codimension zero embeddings and diffeomorphism groups
$Diff(D^n)$ is homotopy equivalent to $O(n)\times Diff(D^n\ rel\ D^{n1})$ where $D^{n1}$ is a disk in $\partial D^n$. The factor $Diff(D^n\ rel\ D^{n1})$ can be identified with the pseudoisotopy space $Diff(D^{n1}\times I\ rel\ D^{n1} \times 0)$, so it has a complicated homotopy type when $n$ is large enough. 
Dec 16 
awarded  Enlightened 
Dec 15 
awarded  Nice Answer 
Dec 14 
revised 
Homotopy versus pathhomotopy on punctured surface
more precise statements 