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Suppose that X is a space and that L is a line bundle on X.A global section of L is a function s : X → L such that if p : L → X is the natural projection, then ps = id X.In a small neighborhood U in X in which L is trivial, the total space of the line bundle is the product of U and the underlying field k, and the section s restricts to a function U → k.
From a topological perspective, there is no difference between sphere bundles and disk bundles: this is a consequence of the Alexander trick, which implies (+) (). An example of a sphere bundle is the torus, which is orientable and has S 1 {\displaystyle S^{1}} fibers over an S 1 {\displaystyle S^{1}} base space.
Vertical and horizontal subspaces for the Möbius strip. The Möbius strip is a line bundle over the circle, and the circle can be pictured as the middle ring of the strip. . At each point on the strip, the projection map projects it towards the middle ring, and the fiber is perpendicular to the middle ri
Deep neurovascular bundles, which often include arteries, have a more complicated structure than superficial neurovascular bundles. Since arteries have high intraluminal blood pressure relative to capillaries and veins, these bundles have smooth muscle and connective tissue structures outside the endothelium. This structure allows arteries to ...
Bachmann's bundle receives its blood supply from the sinoatrial nodal artery (right, left or both). [4]Besides Bachmann's bundle, the other three conduction tracts that constitute the atrial conduction system are known as the anterior, middle, and posterior tracts, which run from the sinoatrial node to the atrioventricular node, converging in the region near the coronary sinus.
In Michael Atiyah's "K-theory", the tautological line bundle over a complex projective space is called the standard line bundle. The sphere bundle of the standard bundle is usually called the Hopf bundle. (cf. Bott generator.) More generally, there are also tautological bundles on a projective bundle of a vector bundle as well as a Grassmann ...
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