Non-operadic operations on loop cohomology

Details Non-operadic operations on loop cohomology Non-operadic operations on loop cohomology

2011-08-29

arxiv.org/abs/1108.5693v8

Mathematics

Algebraic Topology

9 pages. Version 8 fixes an issue in the topological example of Section 3

Scientific paper

We apply the Transfer Algorithm introduced in arXiv:1106.5090 to transfer an A_\infty-algebra structure that cannot be computed using the classical Basic Perturbation Lemma. We construct a space X whose (base pointed) loop cohomology H = H^*(\Omega X; Z_2) comes equipped with a nontrivial operation \omega : H x H --> H x H. This is the first known example of a loop space with an induced non-operadic operation on its cohomology.

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