ists ▁Category : 1 9 th - century ▁German ▁mus icians ▁Category : 1 9 th - century ▁American ▁pian ists ▁Category : E du c ators ▁from ▁Texas ▁Category : Class ical ▁mus icians ▁from ▁Texas ▁Category : 1 9 th - century ▁male ▁mus icians <0x0A> </s> ▁In ▁differential ▁geometry , ▁the ▁integration ▁along ▁fib ers ▁of ▁a ▁k - form ▁yields ▁a ▁- form ▁where ▁m ▁is ▁the ▁dimension ▁of ▁the ▁fi ber , ▁via ▁" integration ". ▁ ▁Definition ▁ ▁Let ▁ ▁be ▁a ▁fi ber ▁bundle ▁over ▁a ▁manifold ▁with ▁compact ▁orient ed ▁fib ers . ▁If ▁ ▁is ▁a ▁k - form ▁on ▁E , ▁then ▁for ▁tang ent ▁vectors ▁w i ' s ▁at ▁b , ▁let ▁▁▁▁ ▁where ▁ ▁is ▁the ▁induced ▁top - form ▁on ▁the ▁fi ber ▁; ▁i . e ., ▁an ▁- form ▁given ▁by : ▁with ▁ ▁lif ts ▁of ▁ ▁to ▁E , ▁ ▁( To ▁see ▁ ▁is ▁smooth , ▁work ▁it ▁out ▁in ▁coordinates ; ▁c f . ▁an ▁example ▁below .) ▁ ▁Then ▁ ▁is ▁a ▁linear ▁map ▁. ▁By ▁Sto kes ' ▁formula , ▁if ▁the ▁fib ers ▁have ▁no ▁boundaries ( i . e . ▁ ▁), ▁the ▁map ▁desc ends ▁to ▁de ▁R ham ▁coh om ology : ▁ ▁This ▁is ▁also ▁called ▁the ▁fi ber ▁integration . ▁ ▁Now , ▁suppose ▁ ▁is ▁a ▁sphere ▁bundle ; ▁i . e ., ▁the ▁typical ▁fi ber ▁is ▁a ▁sphere . ▁Then ▁there ▁is