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William's user avatar
William's user avatar
William
  • Member for 12 years, 9 months
  • Last seen this week
31 votes

What made you choose your research field?

26 votes

What needs to be done to prove that a vector bundle is trivial?

24 votes

Why is the tangent bundle orientable?

16 votes

How to pronounce "$\;\setminus\;$" (the symbol for set difference)

13 votes

Does every short exact sequence split?

12 votes
Accepted

Finding the homology group of $H_n (X,A)$ when $A$ is a finite set of points

9 votes

Quotient Topology

9 votes
Accepted

Existence of section on fiber bundles with contractible fibers.

8 votes

Sum of normal bundle and tangent bundle.

8 votes
Accepted

0 as the unique eigenvalue of a matrix

8 votes

The simplest way of proving that $|\mathcal{P}(\mathbb{N})| = |\mathbb{R}| = c$

7 votes

Is there a non-trivial covering of the Klein bottle by the Klein bottle?

7 votes

Why is it interesting that the fundamental group induces a functor?

7 votes
Accepted

Show that $\mathbb{R}P^5$ and $ \mathbb{R}P^4 \vee S^5$ have the same fundamental group and homology group.

7 votes
Accepted

Prove that $G \cong \pi_{1} (X/G)$.

6 votes
Accepted

What is the "natural homomorphism" in the definition of an *essential manifold*?

6 votes
Accepted

Fundamental group of $X$, a CW complex is isomorphic to the fundamental group of its 2-skeleton

6 votes
Accepted

inclusion of connected manifold of dimension $\geq 3$ minus point induces isomorphism of fundamental groups

6 votes
Accepted

Necessary condition on homology group of a set to be contractible

5 votes
Accepted

Relations between cohomology and homotopy for CW complexes

5 votes
Accepted

Spin structure and bordism

5 votes

How to find the homotopy fiber of bouquet embedding $S^1⋁S^1↪S^1×S^1$

5 votes

Is there a covering space proof of $\pi_1(S^1) \cong \mathbb{Z}$ .

5 votes

Are the rationals a nowhere dense set?

5 votes

What is an effective way to teach children the Cartesian coordinates?

5 votes

$\pi_7(S^4)$ has element of infinite order?

5 votes
Accepted

Which integral Steifel-Whitney classes are universally $0$?

5 votes

Show that $S^2$ and $S^3 \times \mathbb CP^\infty$ have isomorphic homotopy groups.

5 votes
Accepted

Two definitions of singular cohomology

5 votes
Accepted

Does the functor $\pi_n\colon \mathsf{Top}_* \to \mathsf{Grp}$ preserve products?

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