Sequential homology
by
L.J. Hernández Paricio
University of La Rioja, Spain
Coauthors: J. Gracía Calcines (University of La Laguna, Spain)

An exterior space consists of a topological space together with a certain nonempty family of open subsets that is thought of as a `system of open neighborhoods at infinity'. We use sequences of cycles converging to infinity to introduce sequential homology and cohomology theories in the category of exterior spaces. It is interesting to note that the singular homology, the locally finite homology and the end homology can be obtained as sequential homology with coeffients in adequate modules. Similarly, the compact support cohomology, the singular cohomology and the end cohomology are particular cases of sequential cohomology with adequate coefficients. We also analyze the relation with Steenrod homology and give a version of Poincare duality for sequential theories.

Date received: March 7, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cadz-31.