[ALGTOP-L] fundamental infty-groupoid

Marco Grandis grandis at dima.unige.it
Sun Nov 28 04:02:12 EST 2010


Dear Jim,

1. R. Brown has a recent preprint on 'Moore n-paths' for a  
topological space, and
their cubical structure

    R. Brown, Moore hyperrectangles on a space form a strict cubical  
omega-category,
   Preprint (2009). Available at: arXiv:math/0909.2212.

2. The following preprint of mine gives two constructions (Moore and  
standard)
for the singular cubical structure associated to a d-space, i.e. a  
topological space
'with distinguished paths'.
(For a mere topological space, just say that all its paths are  
distinguished.)

Thus, the 'Moore cubes' of a directed space give a strict symmetric  
cubical category,
with concatenation laws in the various directions. On the other hand,  
standard cubes
give a lax cubical structure, where concatenations are associative up  
to invertible
reparametrisation but degeneracies are only lax-unital.

    M. Grandis, A symmetric cubical category associated to a directed  
space.
    Preprint: Dip. Mat. Univ. Genova, Preprint 590 (2010).
        http://www.dima.unige.it/~grandis/Fnd.pdf


Best whishes

Marco Grandis

Dipartimento di Matematica
Università di Genova
Via Dodecaneso, 35
16146 Genova
Italy


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