User Michael Albanese

11 votes

3 answers

433 views

Do $\mathbb{HP}^2\#\overline{\mathbb{HP}^2}$ and $\mathbb{OP}^2\#\overline{\mathbb{OP}^2}$ arise as sphere bundles over spheres?

asked May 31, 2018 at 13:59

11 votes

1 answer

597 views

Is there a closed manifold whose universal cover is $\mathbb{R}^n\setminus\{x_1, \dots, x_k\}$ for some $k > 1$?

asked Mar 30, 2022 at 0:02

9 votes

1 answer

1k views

Non-compact Kähler manifolds which admit a positive line bundle

asked Sep 5, 2012 at 4:33

9 votes

1 answer

933 views

Question about an estimate in Hörmander's proof of Cartan's Theorem B

asked Jun 5, 2012 at 2:38

9 votes

2 answers

1k views

Weitzenböck Identity for $\Delta_{\bar{\partial}_E}$

asked Jul 24, 2013 at 13:01

9 votes

2 answers

1k views

Alternative Almost Complex Structures

asked Mar 26, 2013 at 2:49

8 votes

4 answers

1k views

Hermitian Christoffel Symbols

asked Jun 29, 2012 at 4:31

8 votes

1 answer

628 views

Fundamental groups of non-orientable closed four-manifolds

asked Oct 18, 2017 at 18:45

8 votes

1 answer

709 views

Is there a four-manifold whose tangent bundle is an endomorphism bundle?

asked Apr 18, 2017 at 20:17

8 votes

1 answer

446 views

For each $k$, is there a vector bundle $E$ such that $E\oplus\varepsilon^k$ is trivial but $E\oplus\varepsilon^{k-1}$ is not?

asked Mar 17, 2022 at 0:06

7 votes

1 answer

546 views

Can a hyperbolic manifold be a product?

asked Feb 27, 2019 at 17:51

7 votes

0 answers

351 views

Stiefel-Whitney classes of closed topological manifolds with no smooth structure

asked Jan 24, 2016 at 14:13

7 votes

1 answer

827 views

Where do the Kähler Identities first appear?

asked Dec 17, 2012 at 2:56

7 votes

4 answers

2k views

$E$ is a holomorphic vector bundle if and only if there is a Dolbeault operator $\bar{\partial}_E$

asked Jul 20, 2013 at 4:41

5 votes

1 answer

953 views

Remove a disc from a manifold. When is the resulting sphere nullhomotopic?

asked Sep 29, 2017 at 19:30

4 votes

1 answer

375 views

If $L$ is positive, $E\otimes L^k$ is Nakano positive for some $k$

asked Aug 11, 2013 at 3:11

2 votes

1 answer

216 views

For compact complex surfaces $h^{1,0}$ is either $h^{0,1}$ or $h^{0,1} - 1$. Do we need to use the Enriques-Kodaira classification?

asked Nov 11, 2014 at 1:22

2 votes

1 answer

310 views

Local expression involved in the definition of positivity of vector bundles

asked Jun 20, 2013 at 7:46

1 vote

1 answer

549 views

Decomposition of hermitian form used in the definition of Griffiths/Nakano positivity

asked Jun 11, 2013 at 3:01

Stack Exchange Network

49 Questions

Do $\mathbb{HP}^2\#\overline{\mathbb{HP}^2}$ and $\mathbb{OP}^2\#\overline{\mathbb{OP}^2}$ arise as sphere bundles over spheres?

Is there a closed manifold whose universal cover is $\mathbb{R}^n\setminus\{x_1, \dots, x_k\}$ for some $k > 1$?

Non-compact Kähler manifolds which admit a positive line bundle

Question about an estimate in Hörmander's proof of Cartan's Theorem B

Weitzenböck Identity for $\Delta_{\bar{\partial}_E}$

Alternative Almost Complex Structures

Hermitian Christoffel Symbols

Fundamental groups of non-orientable closed four-manifolds

Is there a four-manifold whose tangent bundle is an endomorphism bundle?

For each $k$, is there a vector bundle $E$ such that $E\oplus\varepsilon^k$ is trivial but $E\oplus\varepsilon^{k-1}$ is not?

Can a hyperbolic manifold be a product?

Stiefel-Whitney classes of closed topological manifolds with no smooth structure

Where do the Kähler Identities first appear?

$E$ is a holomorphic vector bundle if and only if there is a Dolbeault operator $\bar{\partial}_E$

Remove a disc from a manifold. When is the resulting sphere nullhomotopic?

If $L$ is positive, $E\otimes L^k$ is Nakano positive for some $k$

For compact complex surfaces $h^{1,0}$ is either $h^{0,1}$ or $h^{0,1} - 1$. Do we need to use the Enriques-Kodaira classification?

Local expression involved in the definition of positivity of vector bundles

Decomposition of hermitian form used in the definition of Griffiths/Nakano positivity