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aaodNvis abelian algebra base point boundary operator bundle F,B,E carrier chain complex chain homotopy chain map chain module classes of maps closed neighborhood coefficients cohomology operations composition Corollary corresponding defined Definition denote a fiber differential operator dim tt dimension direct sum elements Euclidean space example exists FD-map FD-modules fibre space filtration finite following theorem generalised manifolds geometric hence Hilton Invariants homology structure homology theory homomorphism homotopy classes homotopy manifold homotopy type Hopf invariant Hopf's Hr(x Hurewicz Ihen immersions implies integers isomorphism Lemma LIBRARIES STANFORD UNIVERSITY locally Euclidean main theorem map f map Sd Math maximal kernel ideal n-gm normal obtained pairing prefunctor principal bundle principal ideal Problem Proc proof properties prove pseudogroup regular homotopy regular topological groupoid S3ldVd9ll saiavaan secondary operation singular homology spectral sequence STANFORD UNIVERSITY LIBRARIES Steenrod strong atoms subcomplex subgroupoid subset suspension topological groupoid topological space trivial V-category