User Michael Albanese

84 votes

1 answer

5k views

Is there a complex surface into which every Riemann surface embeds?

asked Oct 27, 2015 at 16:05

38 votes

2 answers

1k views

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

asked Sep 5, 2018 at 20:46

36 votes

2 answers

2k views

Complex manifold with subvarieties but no submanifolds

asked May 2, 2016 at 14:46

29 votes

1 answer

896 views

Is there an explicit description of a cobordism between $\mathbb{CP}^n$ and $\mathbb{RP}^n\times\mathbb{RP}^n$?

asked Feb 16, 2016 at 15:35

29 votes

1 answer

4k views

Almost Complex Structure approach to Deformation of Compact Complex Manifolds

asked Jun 18, 2012 at 15:56

25 votes

1 answer

593 views

Does every large $\mathbb{R}^4$ embed in $\mathbb{R}^5$?

asked May 13, 2019 at 15:24

24 votes

5 answers

4k views

Weitzenböck Identities

asked Sep 14, 2012 at 12:07

24 votes

4 answers

2k views

Examples of compact complex non-Kähler manifolds which satisfy $h^{p,q} = h^{q,p}$

asked Nov 3, 2014 at 23:18

23 votes

2 answers

4k views

Non-compact complex surfaces which are not Kähler

asked Feb 20, 2012 at 5:12

23 votes

3 answers

2k views

Is the analytic version of the Whitney Approximation Theorem true?

asked Apr 22, 2015 at 16:27

23 votes

2 answers

768 views

Does every map $K(\mathbb{Z}, n) \to K(\mathbb{Z}/m, n + k)$ factor through $K(\mathbb{Z}/m, n)$?

asked Aug 24, 2020 at 13:10

23 votes

2 answers

1k views

If the universal cover of a manifold is spin, must it admit a finite cover which is spin?

asked Sep 8, 2020 at 14:31

21 votes

1 answer

1k views

Does every group arise as the fundamental group of a complete Kähler manifold?

asked Mar 4, 2021 at 0:05

21 votes

1 answer

1k views

Are homology spheres stably parallelisable?

asked Jun 16, 2016 at 18:28

20 votes

2 answers

1k views

The first unstable homotopy group of $Sp(n)$

asked Mar 24, 2018 at 19:04

20 votes

3 answers

2k views

Three-dimensional compact Kähler manifolds

asked Jul 8, 2013 at 6:34

19 votes

2 answers

2k views

Does a Kähler manifold always admit a complete Kähler metric?

asked May 24, 2016 at 21:48

18 votes

2 answers

1k views

Does equality of Laplacians imply Kähler?

asked Jun 24, 2012 at 16:27

18 votes

1 answer

980 views

Are Eilenberg-MacLane spaces limits of manifolds?

asked May 22 at 0:04

17 votes

1 answer

644 views

Can the product of an exotic torus and a circle be the standard torus?

asked Nov 22, 2022 at 14:36

17 votes

2 answers

1k views

What is the $\mathbb{Z}_2$ cohomology of an oriented grassmannian?

asked Nov 7, 2018 at 12:32

17 votes

2 answers

636 views

An orientable non-spin${}^c$ manifold with a spin${}^c$ covering space

asked Feb 6, 2018 at 16:37

15 votes

1 answer

839 views

Are there non-smoothable homotopy/homology spheres?

asked Apr 12, 2016 at 18:26

14 votes

0 answers

709 views

Is Hironaka's example the only known deformation of Kähler manifolds with non-Kähler central fibre?

asked Nov 12, 2014 at 6:07

14 votes

1 answer

327 views

Is $\pi_{n-1}$ of a non-trivial connected sum of $n$-manifolds always non-zero?

asked Sep 18, 2017 at 23:50

14 votes

3 answers

973 views

Is the top Stiefel-Whitney number of a topological manifold the Euler characteristic mod two?

asked Sep 10, 2018 at 19:06

14 votes

1 answer

555 views

Is there an orientable prime manifold covered by a non-prime manifold?

asked Jul 1, 2020 at 19:27

12 votes

1 answer

521 views

Does $(S^1\times S^3)\#(S^1\times S^3)\#(S^2\times S^2)$ admit a symplectic form?

asked Apr 14, 2022 at 13:41

12 votes

0 answers

1k views

How much algebraic geometry do I need to study complex geometry?

asked Nov 7, 2014 at 2:31

11 votes

2 answers

3k views

Riemannian metrics as sections of a vector bundle

asked Jul 13, 2012 at 8:29

Stack Exchange Network

49 Questions

Is there a complex surface into which every Riemann surface embeds?

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

Complex manifold with subvarieties but no submanifolds

Is there an explicit description of a cobordism between $\mathbb{CP}^n$ and $\mathbb{RP}^n\times\mathbb{RP}^n$?

Almost Complex Structure approach to Deformation of Compact Complex Manifolds

Does every large $\mathbb{R}^4$ embed in $\mathbb{R}^5$?

Weitzenböck Identities

Examples of compact complex non-Kähler manifolds which satisfy $h^{p,q} = h^{q,p}$

Non-compact complex surfaces which are not Kähler

Is the analytic version of the Whitney Approximation Theorem true?

Does every map $K(\mathbb{Z}, n) \to K(\mathbb{Z}/m, n + k)$ factor through $K(\mathbb{Z}/m, n)$?

If the universal cover of a manifold is spin, must it admit a finite cover which is spin?

Does every group arise as the fundamental group of a complete Kähler manifold?

Are homology spheres stably parallelisable?

The first unstable homotopy group of $Sp(n)$

Three-dimensional compact Kähler manifolds

Does a Kähler manifold always admit a complete Kähler metric?

Does equality of Laplacians imply Kähler?

Are Eilenberg-MacLane spaces limits of manifolds?

Can the product of an exotic torus and a circle be the standard torus?

What is the $\mathbb{Z}_2$ cohomology of an oriented grassmannian?

An orientable non-spin${}^c$ manifold with a spin${}^c$ covering space

Are there non-smoothable homotopy/homology spheres?

Is Hironaka's example the only known deformation of Kähler manifolds with non-Kähler central fibre?

Is $\pi_{n-1}$ of a non-trivial connected sum of $n$-manifolds always non-zero?

Is the top Stiefel-Whitney number of a topological manifold the Euler characteristic mod two?

Is there an orientable prime manifold covered by a non-prime manifold?

Does $(S^1\times S^3)\#(S^1\times S^3)\#(S^2\times S^2)$ admit a symplectic form?

How much algebraic geometry do I need to study complex geometry?

Riemannian metrics as sections of a vector bundle