Schwartz homologies of representations of almost linear Nash groups

Abstract

Let $G$ be an almost linear Nash group, namely, a Nash group which admits a Nash homomorphism with finite kernel to some $\GL_k(\mathbb R)$. A homology theory (the Schwartz homology) is established for the category of smooth \Fre representations of $G$ of moderate growth. Frobenius reciprocity and Shapiro's lemma are proved in this category. As an application, we give a criterion for automatic extensions of Schwartz homologies of Schwartz sections of a tempered $G$-vector bundle.

Mistakes in Theorem 1.15 and Proposition 7.11 of the published version are fixed. Theorems 1.12, 1.13 and 8.5 are slightly improved

References in corpus (1)

• Schwartz functions on Nash manifolds