Michael Albanese's user avatar
Michael Albanese's user avatar
Michael Albanese's user avatar
Michael Albanese
  • Member for 12 years, 1 month
  • Last seen this week
  • Waterloo
31 votes
Accepted

If two smooth manifolds are homeomorphic, then their stable tangent bundles are vector bundle isomorphic

30 votes

What are the possible Stiefel-Whitney numbers of a five-manifold?

28 votes
Accepted

Why is $\mathbb{Z}$ not a Kähler group?

24 votes
Accepted

Does every open orientable even-dimensional smooth manifold admit an almost complex structure?

23 votes

If $M$ and $N$ are closed and $M\times S^1$ is diffeomorphic to $N\times S^1$, is it true that $M$ and $N$ are diffeomorphic?

22 votes
Accepted

Is there a homomorphism between $\pi_8(S^5)$ and $\pi_8(SO(6))$?

22 votes

When can one continuously prescribe a unit vector orthogonal to a given orthonormal system?

21 votes

Examples of common false beliefs in mathematics

20 votes
Accepted

An almost complex structure on $S^2\times ...\times S^2 / \mathbb{Z_2}$

19 votes
Accepted

Is a 4-dimensional submanifold of a spin manifold always spin?

18 votes
Accepted

Converse to Hopf degree theorem

18 votes

Is there a non-trivial group $C$ such that $A*C \cong B*C$ implies $A \cong B$?

16 votes
Accepted

Exact formula for $\chi(X, \, S^n \Omega^1_X)$

16 votes

Maps from 2-Torus to SO(3)

15 votes
Accepted

Exotic $\mathbb{R}^4$ with a complex structure?

14 votes
Accepted

The Hopf Invariant 1 Problem through L-polynomials

14 votes
Accepted

Infinite Grassmannian does not have the homotopy type of a finite-dimensional complex

13 votes
Accepted

Is there a closed 5-manifold $M$ with $w_1(M)w_2(M)\ne 0$?

13 votes

Spin-H structures

13 votes
Accepted

Does the Kähler form $\omega$ satisfy $d^*\omega=0$?

13 votes
Accepted

Stable torus that is not a torus

13 votes

Is a manifold Euclidean if its tangent bundle is Euclidean?

12 votes

Complex vector bundles on compact complex manifolds

12 votes

Complex structure on $S^4$

12 votes

Chern classes of generators of $K(S^{2n})$

12 votes

Complex manifold with subvarieties but no submanifolds

12 votes

Vector bundles on Stein manifolds

12 votes
Accepted

About Sylvester's determinant

11 votes

Pin$^+$ and Pin$^−$ structure for manifolds in any dimensions

11 votes
Accepted

Is a complex vector bundle over a punctured closed surface trivial?