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- W1533976420 abstract "We consider the complex [ begin {CD} 0@>>> {Lambda _ 0(M;E)} @>{partial _ omega }>> {Lambda _ 1(M;E)} @>{partial _omega }>>{dots } @>{partial _omega }>> {Lambda _ m(M;E)}, end {CD} ] where $E$ is a finite-dimensional vector bundle over a suitable differential manifold $M$, $Lambda _ q(M;E)$ denotes the space of all smooth or real analytic or holomorphic sections of the $q$-exterior product of $E$ and $partial _omega (eta ):=omega wedge eta$ for $omega in Lambda _ 1(M;E)$. We give sufficient and necessary conditions for the above complex to be exact and, in smooth and holomorphic cases, we give sufficient conditions for its splitting, i.e., for existence of linear continuous right inverse operators for $partial _omega :Lambda _ q(M;E)to operatorname {Im} partial _omega subseteq Lambda _{q+1}(M;E)$. Analogous results are obtained whenever $M$ is replaced by a suitable closed subset $X$ or $partial _omega$ are replaced by the interior product operators $partial _ Z$, $partial _ Z(eta ):=Zrfloor eta$ for a given section $Z$ of the dual bundle $E^ *$." @default.
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- W1533976420 date "2003-05-09" @default.
- W1533976420 modified "2023-10-18" @default.
- W1533976420 title "Linear continuous division for exterior and interior products" @default.
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- W1533976420 doi "https://doi.org/10.1090/s0002-9939-03-07107-7" @default.
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