RT Journal Article
T1 Topology of the space of conormal distributions
A1 Álvarez López, Jesús Antonio
A1 Kordyukov, Yuri A.
A1 Leichtnam, Eric
K1 (Dual-) conormal distributions
K1 Montel
K1 Complete
K1 Acyclic
K1 Boundedly retractive
K1 Reflexive
AB Given a closed manifold $M$ and a closed regular submanifold $L$, consider the corresponding locally convex space $I=I(M,L)$ of conormal distributions, with its natural topology, and the strong dual $I'=I'(M,L)=I(M,L;\Omega)'$ of the space of conormal densities. It is shown that $I$ is a barreled, ultrabornological, webbed, Montel, acyclic LF-space, and $I'$ is a complete Montel space, which is a projective limit of bornological barreled spaces. In the case of codimension one, similar properties and additional descriptions are proved for the subspace $K\subset I$ of conormal distributions supported in $L$ and for its strong dual $K'$. We construct a locally convex Hausdoff space $J$ and a continuous linear map $I\to J$ such that the sequence $0\to K\to I\to J\to 0$ as well as the transpose sequence $0\to J'\to I'\to K'\to 0$ are short exact sequences in the category of continuous linear maps between locally convex spaces. Finally, it is shown that $I\cap I'=C^\infty(M)$ in the space of distributions. In another publication, these results are applied to prove a Lefschetz trace formula for a simple foliated flow $\phi=\{\phi^t\}$ on a compact foliated manifold $(M,\mathcal F)$. It describes a Lefschetz distribution $L_{\text{\rm dis}}(\phi)$ defined by the induced action $\phi^*=\{\phi^{t\,*}\}$ on the reduced cohomologies $\bar H^\bullet I(\mathcal F)$ and $\bar H^\bullet I'(\mathcal F)$ of the complexes of leafwise currents that are conormal and dual-conormal at the leaves preserved by $\phi$.
PB Birkhäuser (Springer)
YR 2024
FD 2024
LK http://hdl.handle.net/10347/34155
UL http://hdl.handle.net/10347/34155
LA eng
NO Álvarez López, J.A., Kordyukov, Y.A. & Leichtnam, E. Topology of the space of conormal distributions. J. Pseudo-Differ. Oper. Appl. 15, 47 (2024)
NO This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s11868-024-00617-y
NO AEI/FEDER e Xunta de Galicia/FEDER
DS Minerva
RD 23 abr 2026