All questions with tag [math: almost-complex]


Nonintegrable almost complex structures

The Newlander - Nirenberg theory mentions that any kind of Integrable Almost Complex manifold is an intricate manifold. I am seeking all-natural instances of intricate frameworks that are not integrable.
2022-06-08 07:09:23

How can we detect the existence of almost-complex structures?

Any smooth $2n$ - manifold $M$ features a well - specified map $f:M\rightarrow BGL_{2n}(\mathbb{R})$ (approximately homotopy) identifying its tangent package. Given that $GL_{2n}(\mathbb{R})$ contortion - withdraws onto $O(2n)$, $BGL_{2n}(\mathbb{R})\simeq BO(2n)$, which is a charming means of confirming that every smooth manifold confesses a Ri...
2022-06-06 19:07:44