On the Foundation of Algebraic Topology

Details On the Foundation of Algebraic Topology On the Foundation of Algebraic Topology

2004-12-31

arxiv.org/abs/math/0412552v7

Mathematics

Algebraic Topology

64 pages. Corrected typos. Made some clarifications

Scientific paper

In the 70:th, combinatorialists begun to systematically relate simplicial complexes and polynomial algebras, named Stanley-Reisner rings or face rings. This demanded an algebraization of the simplicial complexes, that turned the empty simplicial complex into a zero object w.r.t. to simplicial join, losing its former role as join-unit - a role taken over by a new (-1)-dimensional simplicial complex containing only the empty simplex. There can be no realization functor targeting the classical category of topological spaces that turns the contemporary simplicial join into topological join unless a (-1)-dimensional space is introduced as a topological join-unit. This algebraization of general topology enables a homology theory that unifies the classical relative and reduced homology functors and allows a K\"unneth Theorem for simplicial resp. topological pair-joins.

Affiliated with

Also associated with

No associations

Rating

On the Foundation of Algebraic Topology does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the Foundation of Algebraic Topology, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the Foundation of Algebraic Topology will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346946