Álvarez López, Jesús AntonioKordyukov, Yuri A.Leichtnam, Eric2024-10-042024-10-042024Álvarez López, J.A., Kordyukov, Y.A. & Leichtnam, E. Topology of the space of conormal distributions. J. Pseudo-Differ. Oper. Appl. 15, 47 (2024)1662-9981http://hdl.handle.net/10347/35008Given a closed manifold M and a closed regular submanifold L, consider the correspondinglocally convexspace I = I(M, L)ofconormaldistributions,withitsnatural topology, and the strong dual I = I (M, L) = I(M,L; ) ofthespaceofconormal 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 ⊂ 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 → J such that the sequence 0 → K → I → J → 0aswell as the transpose sequence 0 → J→ I→ K→ 0areshortexact sequences in the category of continuous linear maps between locally convex spaces. Finally, it is shown that I ∩I = C∞(M)inthespaceofdistributions.Inanotherpublication,theseresults are applied to prove a Lefschetz trace formula for a simple foliated flow φ ={φt} on a compact foliated manifold (M,F). It describes a Lefschetz distribution Ldis(φ) defined by the induced action φ∗ ={φt∗} on the reduced cohomologies ¯ H•I(F) and ¯ H•I (F) of the complexes of leafwise currents that are conormal and dual-conormal at the leaves preserved by φ.engAtribución 4.0 Internacional©TheAuthor(s) 2024. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.http://creativecommons.org/licenses/by/4.0/(Dual-) conormal distributionsMontelCompleteBoundedly retractiveReflexivejournal article10.1007/s11868-024-00617-y1662-999Xopen access