(see also Chern-Weil theory, parameterized homotopy theory)
vector bundle, (∞,1)-vector bundle
topological vector bundle, differentiable vector bundle, algebraic vector bundle
direct sum of vector bundles, tensor product of vector bundles, inner product of vector bundles?, dual vector bundle
geometry, complex numbers, complex line
$dim = 1$: Riemann surface, super Riemann surface
The concept of pseudoholomorphic vector bundle (Bryant 05, def. 1) is like that of holomorphic vector bundle but with complex structures relaxed to almost complex structures.
Robert Bryant, Remarks on the geometry of almost complex 6-manifolds, The Asian Journal of Mathematics, vol. 10 no. 3 (September, 2006), pp. 561–606 (arXiv:math/0508428, Euclid)
Boris Kruglikov, Tangent and normal bundles in almost complex geometry (arXiv:math/0304165)
Boris Kruglikov, Symmetries of almost complex structures and pseudoholomorphic foliations, International Journal of Mathematics 2014; Volume 25 (8) (arXiv:1103.4404)
Alexander D. Popov, Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds, Nucl.Phys.B828:594-624, 2010 (arXiv:0907.0106)
Last revised on August 10, 2017 at 18:06:28. See the history of this page for a list of all contributions to it.