Let R be a ring containing 1/m for m < p. Let A be an E3 algebra over R concentrated in the degree range r + 1 ≤ n ≤ rp − p + 1. Then, as an E 2 algebra, A is equivalent to a commutative algebra. As a consequence, if X is an r connected, rp − p + 1 dimensional, finite simplicial set, then S*(X, R), the singular cochain complex over the ring R, is equivalent as an E2 algebra to a commutative algebra.
|Advisor:||Mandell, Michael A.|
|Commitee:||Davis, James F., Lindenstrauss, Ayelet, Strauch, Matthias|
|School Location:||United States -- Indiana|
|Source:||DAI-B 74/02(E), Dissertation Abstracts International|
|Keywords:||Algebraic topology, Cochains, Homotopy, Operad|
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