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bio website math.cornell.edu/~hatcher
location Cornell University
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visits member for 5 years, 8 months
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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
Feb
5
awarded  Nice Answer
Feb
5
answered Maps which induce the same homomorphism on homotopy and homology groups are homotopic