The topology of certain 3-Sasakian 7-manifolds

Details The topology of certain 3-Sasakian 7-manifolds The topology of certain 3-Sasakian 7-manifolds

2005-11-30

arxiv.org/abs/math/0511735v2

Math. Ann. 339 (2007), no. 4, 733-755

Mathematics

Algebraic Topology

24 pages

Scientific paper

We calculate the integer cohomology ring and stable tangent bundle of a family of compact, 3-Sasakian 7-manifolds constructed by Boyer, Galicki, Mann, and Rees. Previously only the rational cohomology ring was known. The most important part of the cohomology ring is a torsion group that we describe explicitly and whose order we compute. There is a surprising connection with the combinatorics of trees.

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