We show that the additive category of chain complexes parametrized by a finite simplicial complex K forms a category with chain duality. This fact, never fully proven in the original reference (Ranicki, 1992), is fundamental for Ranicki's algebraic formulation of the surgery exact sequence of Sullivan and Wall, and his interpretation of the surgery obstruction map as the passage from local Poincaré duality to global Poincaré duality.
1
Indiana University, Bloomington, USA
2
Loyola University Chicago, USA
James F. Davis; Carmen Rovi. Chain duality for categories over complexes. EMS surveys in mathematical sciences, Tome 9 (2022) no. 2, pp. 477-505. doi: 10.4171/emss/65
@article{10_4171_emss_65,
author = {James F. Davis and Carmen Rovi},
title = {Chain duality for categories over complexes},
journal = {EMS surveys in mathematical sciences},
pages = {477--505},
year = {2022},
volume = {9},
number = {2},
doi = {10.4171/emss/65},
url = {http://geodesic.mathdoc.fr/articles/10.4171/emss/65/}
}
TY - JOUR
AU - James F. Davis
AU - Carmen Rovi
TI - Chain duality for categories over complexes
JO - EMS surveys in mathematical sciences
PY - 2022
SP - 477
EP - 505
VL - 9
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/emss/65/
DO - 10.4171/emss/65
ID - 10_4171_emss_65
ER -
%0 Journal Article
%A James F. Davis
%A Carmen Rovi
%T Chain duality for categories over complexes
%J EMS surveys in mathematical sciences
%D 2022
%P 477-505
%V 9
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/emss/65/
%R 10.4171/emss/65
%F 10_4171_emss_65
