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2h

awarded  Good Answer 
17h

comment 
Does every connected component of a covering space over a connected base intersect all the fibers of the covering space?
The question should be rephrased to eliminate the ambiguity of what the word "its" refers to. (Does it refer to "connected component" or to "covering space"?) 
Sep
25 
answered  Cup product of cohomology in a Serre spectral sequence 
Sep
23 
comment 
Are there noncontractible spaces $A$ and $B$ such that $A \wedge B$ is contractible?
In the same spirit, just take the smash product of two CW complexes that are Moore spaces for finite cyclic groups of relatively prime orders. 
Sep
21 
revised 
What are the possible automorphism groups of Riemann surfaces of low genus?
added 724 characters in body 
Sep
21 
answered  What are the possible automorphism groups of Riemann surfaces of low genus? 
Sep
4 
comment 
characteristic classes of homotopy equivalent manifolds
The question as originally stated assumes the two manifolds have different dimensions. If this is what was intended, then the manifolds cannot both be closed, and counterexamples are easy to find. For example, let $M$ be the circle and $N$ the Moebius band (either the compact or the noncompact version). These have different classes $w_1$ since $M$ is an orientable manifold and $N$ is not. Higherdimensional counterexamples are equally easy to find. 
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 KervaireMilnor 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 Jhomomorphism. 
Aug
26 
awarded  Nice Answer 
Jul
31 
comment 
Manifold approximations to $BO(3)$
For $BO(3)$ one can choose the Grassmannian of 3planes in ${\mathbb R}^\infty$, and this is in some sense approximated by the finitedimensional Grassmann manifolds of 3planes 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 LeraySerre 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.geometrictopology 
Apr
4 
answered  Topological $n$manifolds have the homotopy type of $n$dimensional CWcomplexes 
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 onetoone 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 pathconnected, this means $f$ and $g$ are homotopic. 