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These operations in the singular setting were fully and explicitly developed and generalized beautifully by McClure and Smith (who also credit Benson and Milgram): Milgram) in their paper "Multivariable cochain operations and little $n$-cubes": http://arxiv.org/pdf/math.QA/0106024.pdf

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These operations in the singular setting were fully and explicitly developed and generalized beautifully by McClure and Smith (who also credit Benson and Milgram): http://arxiv.org/pdf/math.QA/0106024.pdf

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These operations were fully and explicitly developed and generalized beautifully by McClure and Smith (who also credit Benson and Milgram): http://arxiv.org/pdf/math.QA/0106024.pdf