AUTHOR: Ronald Brown

AUTHOR ADDRESS:  School of Computer Science, University of Wales, Dean St., Bangor, Gwynedd, LL57 1UT, UK;
email: r.brown@bangor.ac.uk

TITLE: A new higher homotopy groupoid: the fundamental  globular omega-groupoid 
  of a filtered space
  
MSC Classification:18D10, 18G30, 18G50, 20L05, 55N10, 55N25.

KEY WORDS: filtered space, higher homotopy van Kampen theorem,
cubical singular complex, free globular  groupoid

xxxLANL archive: math.AT/0702677

2 eps files, 19 pages


ABSTRACT: 
We show that the graded set of filter homotopy classes rel vertices of maps from the n-globe 
to a filtered space may be given the structure of globular omega--groupoid. The
proofs use an analogous fundamental cubical omega--groupoid due
to the author and Philip Higgins. This method also relates the
construction to the fundamental crossed complex of a filtered space,
and this relation allows the proof that the crossed complex
associated to the free globular omega-groupoid on one element of
dimension n is the fundamental crossed complex of the n-globe.