Higher holonomies: comparing two constructions

Publication: Research - peer-reviewJournal article

  • Florian Schaetz
    Florian SchaetzDenmark
  • Camilo Arias Abad
    Camilo Arias AbadMax-Planck Institute for Mathematics, BonnGermany
We compare two different constructions of higher-dimensional parallel transport. On the one hand, there is the two-dimensional parallel transport associated with 2-connections on 2-bundles studied by Baez–Schreiber [2], Faria Martins–Picken [11] and Schreiber–Waldorf [12]. On the other hand, there are the higher holonomies associated with flat superconnections as studied by Igusa [7], Block–Smith [3] and Arias Abad–Schätz [1]. We first explain how by truncating the latter construction one obtains examples of the former. Then we prove that the two-dimensional holonomies provided by the two approaches coincide.
Original languageEnglish
JournalDifferential Geometry and Its Applications
Volume40
Pages (from-to)14-42
Number of pages29
ISSN0926-2245
DOIs
StatePublished - 3 Mar 2015

    Keywords

  • flat superconnections, 2-holonomy, higher holonomies, crossed modules

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