Geodesic
Comparing the orthogonal and unitary functor calculi
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 227-256.

Voir la notice de l'article provenant de la source International Press of Boston

The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces. We construct functors between the calculi from the complexification-realification adjunction between real and complex inner product spaces. These allow for movement between the versions of calculi, and comparisons between the Taylor towers produced by both calculi. We show that when the inputted orthogonal functor is weakly polynomial, the Taylor tower of the functor restricted through realification and the restricted Taylor tower of the functor agree up to weak equivalence. We further lift the homotopy level comparison of the towers to a commutative diagram of Quillen functors relating the model categories for orthogonal calculus and the model categories for unitary calculus.
DOI : 10.4310/HHA.2021.v23.n2.a13
Classification : 55P42, 55P65, 55P91, 55U35
Keywords: functor calculus, orthogonal calculus, unitary calculus, G-spectra 
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     pages = {227--256},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a13/}
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Niall Taggart. Comparing the orthogonal and unitary functor calculi. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 227-256. doi : 10.4310/HHA.2021.v23.n2.a13. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a13/

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