Question

For any two almost complex structures on infinite-dimensional space: Do they give isomorphic vector spaces? Are they similar?

score 162 · Answer 1 · 2026-03-25 17:37:34

162

Views

For any two almost complex structures on infinite-dimensional space: Do they give isomorphic vector spaces? Are they similar?

Published on 25 Mar 2026 - 17:37

score 169 · Answer 2 · 2026-03-25 16:06:12

169

Views

Finding an almost complex structure (aka anti-involution) given an involution

Published on 25 Mar 2026 - 16:06

score 799 · Answer 3 · 2026-03-25 07:42:18

799

Views

Dimension of the complex projective space $\mathbb{C}\mathbb{P}^n$ as almost complex manifold

Published on 25 Mar 2026 - 7:42

score 54 · Answer 4 · 2026-03-25 14:26:02

54

Views

Is there a reasonable notion of a totally real Grassmannian?

Published on 25 Mar 2026 - 14:26

score 318 · Answer 5 · 2026-05-10 17:08:54

318

Views

A complex vector bundle $E$ is a holomorphic vector bundle iff $(\overline{\partial^E})^2=0$ help with proof?

Published on 10 May 2026 - 17:08

score 260 · Answer 6 · 2026-03-25 14:23:50

260

Views

Fundamental form of almost complex manifold is $(1,1)$-form

Published on 25 Mar 2026 - 14:23

score 317 · Answer 7 · 2026-03-25 15:57:16

317

Views

Real $2n$-plane bundle with a complex structure is a complex $n$-plane bundle

Published on 25 Mar 2026 - 15:57

score 34 · Answer 8 · 2026-03-25 17:37:46

34

Views

Relative version of identity theorem for pseudoholomorphic curves

Published on 25 Mar 2026 - 17:37

score 510 · Answer 9 · 2026-03-25 16:02:27

510

Views

The first chern class of $O(1)$ is positive

Published on 25 Mar 2026 - 16:02

score 156 · Answer 10 · 2026-03-25 17:34:56

156

Views

Chern classes and almost complex submanifolds

Published on 25 Mar 2026 - 17:34

score 1.1k · Answer 11 · 2026-03-25 11:17:51

1.1k

Views

Holomorphic vector bundles on almost complex manifolds

Published on 25 Mar 2026 - 11:17

score 290 · Answer 12 · 2026-03-25 16:03:03

290

Views

Coordinates for a neighborhood of a totally real submanifold

Published on 25 Mar 2026 - 16:03

score 202 · Answer 13 · 2026-03-25 15:59:53

202

Views

Given almost complex structure of $V$, there is a symplectic form

Published on 25 Mar 2026 - 15:59

score 117 · Answer 14 · 2026-03-25 19:03:34

117

Views

Making sense of $\frac{\mathrm{GL}(2n,\mathbb{R})}{\mathrm{GL}(n,\mathbb{C})}$

Published on 25 Mar 2026 - 19:03

score 724 · Answer 15 · 2026-03-25 16:06:01

724

Views

Almost complex structures and multiplication by $i$

Published on 25 Mar 2026 - 16:06

List Question

For any two almost complex structures on infinite-dimensional space: Do they give isomorphic vector spaces? Are they similar?

Finding an almost complex structure (aka anti-involution) given an involution

Dimension of the complex projective space $\mathbb{C}\mathbb{P}^n$ as almost complex manifold

Is there a reasonable notion of a totally real Grassmannian?

A complex vector bundle $E$ is a holomorphic vector bundle iff $(\overline{\partial^E})^2=0$ help with proof?

Fundamental form of almost complex manifold is $(1,1)$-form

Real $2n$-plane bundle with a complex structure is a complex $n$-plane bundle

Relative version of identity theorem for pseudoholomorphic curves

The first chern class of $O(1)$ is positive

Chern classes and almost complex submanifolds

Holomorphic vector bundles on almost complex manifolds

Coordinates for a neighborhood of a totally real submanifold

Given almost complex structure of $V$, there is a symplectic form

Making sense of $\frac{\mathrm{GL}(2n,\mathbb{R})}{\mathrm{GL}(n,\mathbb{C})}$

Almost complex structures and multiplication by $i$

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