## Generalized homology and the generalized vector field problem |

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### Contents

3 ?b homology of Products of Projective Spaces | 10 |

5 Identification of the Class of the Axial Map | 29 |

Nonexistence of Axial Maps | 37 |

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### Common terms and phrases

4b+l A-modules Adams operation Adams spectral sequence algebra axial class axial map b^-homology cofibration sequence cohomology complexification map component D-sequences direct sum Doctor of Philosophy dual elements example exp2(j+l exterior algebra ExtQ factor filtration zero free modules G^-modules gN0NE gNONE hence homology homotopy groups Hopf Im(Sq Sq independent sections isomorphism J. F. Adams Lemma mapping cone Massey products Math minimal G^-generating set mod k values multiplication non-zero number of sections obtain P A P A P P1 x PJ PJ A PT Proposition 7-5 R. J. Milgram real projective space result s(gN sequence of towers short exact sequence similarly smash product spectrum splitting unless Sq e e e Sq Sq g Sq Sq Sq summand Theorem 2.1k Theorem 3-9 tower arises unit as coefficient universal coefficient universal coefficient theorem vector field problem X A 2bQ yields