▁of ▁differential ▁forms ▁on ▁E ▁with ▁vertical - comp act ▁support . ▁If ▁E ▁is ▁orient ed ▁as ▁a ▁vector ▁bundle , ▁exactly ▁as ▁before , ▁we ▁can ▁define ▁the ▁integration ▁along ▁the ▁fi ber : ▁ ▁The ▁following ▁is ▁known ▁as ▁the ▁projection ▁formula . ▁We ▁make ▁ ▁a ▁right ▁- module ▁by ▁setting ▁. ▁ ▁Proof : ▁ 1 . ▁Since ▁the ▁assertion ▁is ▁local , ▁we ▁can ▁assume ▁ π ▁is ▁trivial : ▁i . e ., ▁ ▁is ▁a ▁projection . ▁Let ▁ ▁be ▁the ▁coordinates ▁on ▁the ▁fi ber . ▁If ▁, ▁then , ▁since ▁ ▁is ▁a ▁ring ▁hom omorphism , ▁ ▁Similarly , ▁both ▁sides ▁are ▁zero ▁if ▁α ▁does ▁not ▁contain ▁dt . ▁The ▁proof ▁of ▁ 2 . ▁is ▁similar . ▁ ▁See ▁also ▁ ▁Trans gression ▁map ▁ ▁Notes ▁ ▁References ▁ ▁M iche le ▁Aud in , ▁Tor us ▁actions ▁on ▁sym ple ctic ▁manif olds , ▁B irk haus er , ▁ 2 0 0 4 ▁ ▁Category : D iffer ential ▁geometry <0x0A> </s> ▁Songs ▁From ▁the ▁Gy ps y ▁is ▁the ▁sixth ▁album ▁by ▁Min ne apolis ▁C elt ic ▁rock ▁band ▁Bo iled ▁in ▁Le ad , ▁and ▁its ▁second ▁with ▁lead ▁singer / gu itar ist ▁Adam ▁St em ple . ▁It ▁is ▁a ▁song ▁cycle ▁based ▁on ▁a ▁Hung arian ▁folk ▁tale , ▁written ▁largely ▁by ▁St em ple ▁and ▁his ▁C ats ▁L aug hing ▁band mate ▁Steven ▁Br ust ▁several ▁years ▁prior ▁to ▁Bo