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Popaths and Holinks
#
Popaths and Holinks

##
David A. Miller

In the study of stratified spaces it is useful to examine spaces of
popaths (paths which travel from lower strata to higher strata) and
holinks (those spaces of popaths which immediately leave a lower stratum
for their final stratum destination). It is not immediately clear
that for adjacent strata these two path spaces are homotopically
equivalent, and even less clear that this equivalence can be
constructed in a useful way (with a deformation of the space of
popaths which fixes start and end points and where popaths instantly
become members of the holink). The advantage of such an equivalence
is that it allows a stratified space to be viewed categorically
because popaths, unlike holink paths (which are easier to study),
can be composed. This paper proves the aforementioned equivalence in
the case of Quinn's homotopically stratified spaces [1].

Journal of Homotopy and Related Structures, Vol. 4(2009), No. 1, pp. 265-273