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
â†’ 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.