Lefschetz-Pontrjagin duality for differential characters

Citation
R. Harvey et B. Lawson, Lefschetz-Pontrjagin duality for differential characters, AN AC BRASI, 73(2), 2001, pp. 145-159
Citations number
11
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
ANAIS DA ACADEMIA BRASILEIRA DE CIENCIAS
ISSN journal
0001-3765 → ACNP
Volume
73
Issue
2
Year of publication
2001
Pages
145 - 159
Database
ISI
SICI code
0001-3765(200106)73:2<145:LDFDC>2.0.ZU;2-A
Abstract
A theory of differential characters is developed for manifolds with boundar y, This is done from both the Cheeger-Simons and the deRham-Federer viewpoi nts. The central result of the paper is the formulation and proof of a Lefs chetz-Pontrjagin Duality Theorem, which asserts that the pairing (H) over cap (k)(X, partial derivativeX) x (H) over cap (n-k-1)(X) --> S-1 given by (alpha, beta) --> (alpha * beta) [X] induces isomorphisms D : (H) over cap (k)(X, partial derivativeX) --> Hom(infinity)((H) over cap (n-k-1) (X), S-1) D': (H) over cap (n-k-1)(X) --> Hom(infinity)((H) over cap (k)(X, partial d erivativeX), S-1) onto the smooth Pontrajagin duals. In particular, D and D' are injective wi th dense range in the group of all continuous homomorphisms into the circle . A coboundary map is introduced which yields a long sequence for the chara cter groups associated to the pair (X, partial derivativeX), The relation o f the sequence to the duality mappings is analyzed.