Homotopy Transition Cocycles

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dc.creatorWirth, James
dc.creatorStasheff, Jim
dc.date2006-09-07
dc.date2006-09-11
dc.date.accessioned2026-07-07T07:24:38Z
dc.date.available2026-07-07T07:24:38Z
dc.descriptionFor locally homotopy trivial fibrations, one can define transition functions $$ g\dab : U\da\cap U\db \to H = H(F)$$ where $H$ is the monoid of homotopy equivalences of $F$ to itself but, instead of the cocycle condition, one obtains only that $g\dab g\dbgam$ is homotopic to $g\dagam$ as a map of $U\da\cap U\db\cap U\dgam$ into $H$. Moreover on multiple intersections, higher homotopies arise and are relevant to classifying the fibration. The full theory was worked out by the first author in his 1965 Notre Dame thesis \cite{wirth:diss}. Here we present it using language that has been developed in the interim. We also show how this points a direction `on beyond gerbes'.
dc.description14 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0609220
dc.identifierhttp://arxiv.org/abs/math/0609220
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/116432
dc.subjectAlgebraic Topology
dc.subjectAlgebraic Geometry
dc.subjectCategory Theory
dc.subject55R35,55R15,55R10,55R05,55P65,55P99
dc.titleHomotopy Transition Cocycles
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