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We develop some methods to compute the Makar-Limanov and Derksen invariants,isomorphism classes and automorphism groups for k-domains B, which areconstructed from certain Russell k-domains. We propose tools and techniques todistinguish between k-domains with the same Makar-Limanov and Derkseninvariants. In particular, we introduce the exponential chain associated tocertain modifications. We extract C-domains from the class B that have smoothcontractible factorial Spec(B), which are diffeomorphic to R 6 but notisomorphic to C 3, that is, exotic C 3. We examine associated exponentialchains to prove that exotic threefolds Spec(B) are not isomorphic to Spec(R),for any Russell C-domain R.

Methods to compute ring invariants and applications: a new class of exotic threefolds