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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Configuration spaces of products


Authors: William Dwyer, Kathryn Hess and Ben Knudsen
Journal: Trans. Amer. Math. Soc. 371 (2019), 2963-2985
MSC (2010): Primary 18D50, 55R80
DOI: https://doi.org/10.1090/tran/7617
Published electronically: November 16, 2018
MathSciNet review: 3896102
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Abstract: We show that the configuration spaces of a product of parallelizable manifolds may be recovered from those of the factors as the Boardman-Vogt tensor product of right modules over the operads of little cubes of the appropriate dimension. We also discuss an analogue of this result for manifolds that are not necessarily parallelizable, which involves a new operad of skew little cubes.


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Additional Information

William Dwyer
Affiliation: Department of Mathematics, University of Notre Dame, 255 Hurley, Notre Dame, Indiana 46556

Kathryn Hess
Affiliation: EPFL, Bâtiment MA, Station 8, CH-1015 Lausanne, Switzerland

Ben Knudsen
Affiliation: Mathematics Department, Harvard University, Cambridge, Massachusetts 02138

DOI: https://doi.org/10.1090/tran/7617
Received by editor(s): October 13, 2017
Received by editor(s) in revised form: March 5, 2018
Published electronically: November 16, 2018
Article copyright: © Copyright 2018 American Mathematical Society