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 Boundedly retractive
K1 Reflexive
AB Given 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.
PB Springer
SN 1662-9981
YR 2024
FD 2024
LK http://hdl.handle.net/10347/35008
UL http://hdl.handle.net/10347/35008
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 The authors are partially supported by the Grants MTM2017-89686-P and PID2020-114474GB-I00 (AEI/FEDER, UE) and ED431C 2019/10 (Xunta de Galicia, FEDER).
DS Minerva
RD 25 abr 2026