Question

Different almost complex structures: $\mathbb C$-isomorphism for $(W,K)$ and $(W,H)$

score 113 · Answer 1 · 2026-03-25 14:21:23

113

Views

Different almost complex structures: $\mathbb C$-isomorphism for $(W,K)$ and $(W,H)$

Published on 25 Mar 2026 - 14:21

score 482 · Answer 2 · 2026-03-25 15:59:55

482

Views

Complexification of a map under nonstandard complexifications of vector spaces

Published on 25 Mar 2026 - 15:59

score 788 · Answer 3 · 2026-03-25 16:02:57

788

Views

$f$ is the complexification of a map if $f$ commutes with almost complex structure and standard conjugation. What if we had anti-commutation instead?

Published on 25 Mar 2026 - 16:02

score 240 · Answer 4 · 2026-03-25 14:24:37

240

Views

$f$ is the complexification of a map if $f$ commutes with structure $J$ and conjugation $\chi$. What is the relationship between $J$ and $\chi$?

Published on 25 Mar 2026 - 14:24

score 218 · Answer 5 · 2026-03-25 14:24:38

218

Views

In what way is $(L_{\mathbb R})^{\mathbb C}$ more like $L \bigoplus \overline L$ than like $L \bigoplus L = L^2$?

Published on 25 Mar 2026 - 14:24

score 408 · Answer 6 · 2026-03-25 15:58:52

408

Views

Complexification of realification: Unnecessary computation of eigenvalues?

Published on 25 Mar 2026 - 15:58

score 541 · Answer 7 · 2026-03-25 14:21:34

541

Views

Eigenvalues and eigenspaces of almost complex structures under each other

Published on 25 Mar 2026 - 14:21

score 130 · Answer 8 · 2026-03-25 14:21:06

130

Views

Questions on the complexification of a map

Published on 25 Mar 2026 - 14:21

score 277 · Answer 9 · 2026-03-25 16:00:04

277

Views

Are anti-linear/semi-linear maps, such as conjugations, linear in other almost complex structures?

Published on 25 Mar 2026 - 16:00

score 119 · Answer 10 · 2026-03-25 14:20:56

119

Views

Restriction of complexification is almost complex but not conversely?

Published on 25 Mar 2026 - 14:20

score 208 · Answer 11 · 2026-03-25 16:06:59

208

Views

Existence of subspaces such that almost complex structures restrict to almost complex structures

Published on 25 Mar 2026 - 16:06

score 934 · Answer 12 · 2026-03-25 16:02:11

934

Views

What exactly is the relationship between the concepts of conjugate complex vector space and conjugations/real structures?

Published on 25 Mar 2026 - 16:02

score 206 · Answer 13 · 2026-03-25 14:27:19

206

Views

Bijection for involutive maps and $\mathbb R$-subspaces given almost complex structure (anti-involutive)? Formula for conjugation?

Published on 25 Mar 2026 - 14:27

score 191 · Answer 14 · 2026-03-25 19:06:29

191

Views

Formula for anti-involutive (almost complex structures) and involutive maps on any $V^2$ in terms of linear maps on $V$ based on $\mathbb R^2$

Published on 25 Mar 2026 - 19:06

score 77 · Answer 15 · 2026-03-25 14:25:48

77

Views

If subspace $A$ is the fixed points of an involution $\sigma$, then is $K(A)$ the fixed points of $-\sigma$?

Published on 25 Mar 2026 - 14:25

List Question

Different almost complex structures: $\mathbb C$-isomorphism for $(W,K)$ and $(W,H)$

Complexification of a map under nonstandard complexifications of vector spaces

$f$ is the complexification of a map if $f$ commutes with almost complex structure and standard conjugation. What if we had anti-commutation instead?

$f$ is the complexification of a map if $f$ commutes with structure $J$ and conjugation $\chi$. What is the relationship between $J$ and $\chi$?

In what way is $(L_{\mathbb R})^{\mathbb C}$ more like $L \bigoplus \overline L$ than like $L \bigoplus L = L^2$?

Complexification of realification: Unnecessary computation of eigenvalues?

Eigenvalues and eigenspaces of almost complex structures under each other

Questions on the complexification of a map

Are anti-linear/semi-linear maps, such as conjugations, linear in other almost complex structures?

Restriction of complexification is almost complex but not conversely?

Existence of subspaces such that almost complex structures restrict to almost complex structures

What exactly is the relationship between the concepts of conjugate complex vector space and conjugations/real structures?

Bijection for involutive maps and $\mathbb R$-subspaces given almost complex structure (anti-involutive)? Formula for conjugation?

Formula for anti-involutive (almost complex structures) and involutive maps on any $V^2$ in terms of linear maps on $V$ based on $\mathbb R^2$

If subspace $A$ is the fixed points of an involution $\sigma$, then is $K(A)$ the fixed points of $-\sigma$?

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