Mappings of H-spaces



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The spaces considered throughout are H-spaces and the maps are usually H-maps, fibrations or cofibrations. In the first part of this dissertation conditions which preserve homotopy associativity and homotopy commutativity of H-spaces are obtained. Also a non-trivial product similar to the Whitehead product is defined on the groups of homotopy classes of maps into H-spaces. Next, pullbacks of H-spaces are considered and it is shown that if the maps are H-roap fibrations then the space obtained is an H-space. An example is given to show that this is not true for pushouts of H-spaces. Dual questions are considered for co-H spaces. It is shown that covering spaces over H-spaces must inherit an H-structure but spaces covered by an H-space do not necessarily have to be H-spaces. Finally, weak homotopy equivalence is considered. If Y is an H-space and X is weakly homotopy equivalent to Y necessary conditions are found in order that X be an H-space.