bio | website | math.cornell.edu/~hatcher |
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location | Cornell University | |
age | ||
visits | member for | 5 years, 9 months |
seen | 1 hour ago | |
stats | profile views | 2,864 |
Aug
26 |
comment |
Parallelizability of the Milnor's exotic spheres in dimension 7
The stable parallelizability of exotic spheres is Theorem 3.1 of the famous Kervaire-Milnor paper "Groups of homotopy spheres I" in the 1963 Annals. The proof is short but uses several big theorems from the previous decade such as Bott periodicity, the Hirzebruch signature theorem, and Adams' work on the J-homomorphism. |
Aug
26 |
awarded | Nice Answer |
Jul
31 |
comment |
Manifold approximations to $BO(3)$
For $BO(3)$ one can choose the Grassmannian of 3-planes in ${\mathbb R}^\infty$, and this is in some sense approximated by the finite-dimensional Grassmann manifolds of 3-planes in ${\mathbb R}^n$. What kind of approximation do you have in mind? |
Jul
26 |
answered | Essential surfaces in the Exterior of Montesinos knots |
Jul
14 |
awarded | Good Answer |
May
11 |
answered | Multiplicative structure in the cohomological Leray-Serre spectral sequence - please elucidate a proof |
May
3 |
comment |
A Jordan Separation Theorem for Polyhedral Surfaces
The third condition in the definition of a polyhedral surface currently reads: "If an edge of a polygon in C intersects an edge of another polygon in C in a common vertex, then the two edges are also edges of a third polygon in C." This seems too restrictive since it excludes vertices of valence greater than three. Lee Mosher's answer gives the correct condition. |
Apr
5 |
awarded | gt.geometric-topology |
Apr
4 |
answered | Topological $n$-manifolds have the homotopy type of $n$-dimensional CW-complexes |
Mar
31 |
revised |
How can i change 8_19 to (3,4)-torus knot K(3,4)?
added 279 characters in body |
Mar
31 |
answered | How can i change 8_19 to (3,4)-torus knot K(3,4)? |
Feb
24 |
comment |
Maps of balls with fixed value along boundary
On the other hand, if you wish to allow only homotopies $f_t$ and $g_t$ such that $f_t=g_t$ on $S^2$ for all $t$, then such pairs $(f,g)$ are equivalent to maps $h:S^3\to X$. Homotopy classes of maps $h:S^3\to X$ without basepoint conditions are in one-to-one correspondence with orbits of the action of $\pi_1(X)$ on $\pi_3(X)$, and this set of orbits can be nontrivial. |
Feb
24 |
comment |
Maps of balls with fixed value along boundary
If you do not require $f=g$ on $S^2$ during homotopies, then the problem becomes trivial since every map $B^3\to X$ is homotopic to a constant map. Since we may assume $X$ is path-connected, this means $f$ and $g$ are homotopic. |
Feb
23 |
answered | Maps of balls with fixed value along boundary |
Feb
16 |
awarded | Nice Answer |
Feb
15 |
answered | Homology equivalence and isomorphism on $\pi_1$ not enough for homotopy equivalence? |
Feb
11 |
comment |
Inserting an open and simply-connected set between a compact set and an open set
Interesting use of language here (twice) that I don't recall seeing before: "If [X], if [Y], then [Z]." Is this equivalent to "If [X] and [Y], then [Z]"? Or maybe "If [X] such that [Y], then [Z]". |
Feb
9 |
awarded | Guru |
Feb
6 |
awarded | Good Answer |
Feb
5 |
awarded | Enlightened |