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Splitting off tori and the evaluation subgroup of the fundamental group

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Abstract

Given a spaceX what is the largest torusT n such thatX is homotopy equivalent toY×T n We find the answer depends on a simple property of the evaluation subgroup of the fundamental group,G 1(X). As corollaries we have the Splitting theorem of Conner and Raymond and the fact that the dimension ofX must be greater than the rank ofG 1(X).

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Authors and Affiliations

  1. Purdue University, W. Lafayette, Indiana, USA

    Daniel Henry Gottlieb

  2. I.H.E.S., Bures-sur-Yvette, France

    Daniel Henry Gottlieb

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  1. Daniel Henry Gottlieb
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Gottlieb, D.H. Splitting off tori and the evaluation subgroup of the fundamental group. Israel J. Math. 66, 216–222 (1989). https://doi.org/10.1007/BF02765893

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  • DOI: https://doi.org/10.1007/BF02765893

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