MOSTAFA ESFAHANI ZADEH

InthispaperwestateandprovedelocalizedMorsetypeinequalitiesforMorsefunctions aswellasforcloseddi?erential1-forms.TheseinequalitiesinvolvedelocalizedBettinumbers.Asanimmediateconsequence,weprovethevanishingofdelocalizedBettinumbersofmanifoldsfiberingoverthecircleunderavanishingconditiononthedelocalizingconjugacyclass.