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In this paper we analyse the higher topological Hochschild homology of commutative Thom  S ‐algebras. This includes the case of the classical cobordism spectra  MO ,  MSO ,  MU , etc. We consider the homotopy orbits of the torus action on iterated topological Hochschild homology and we describe the relationship to topological André‐Quillen homology.

Higher topological Hochschild homology of Thom spectra