English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We introduce a new variant of Hochschild's two-sided bar construction for thesetting of curved differential graded algebras. One can geometrically think ofthe classical bar complex as elements from the algebra positioned alongdifferent points in the closed interval $[0,1]$. In this paper, we start with acurved differential graded algebra and define a new ``zigzag algebra'' that,informally, consists of algebra elements arranged on a zigzag of intervalsgoing back and forth between $0$ and $1$. We focus on two curved differentialgraded algebras: the de Rham algebra of differential forms with values in theendomorphism bundle associated to a vector bundle with connection, and itsinduced zigzag algebra. We define a curved version of Chen's iterated integralthat incorporates parallel transport and maps this zigzag algebra ofbundle-valued forms to bundle-valued forms on the path space. This iteratedintegral is proven to be a homotopy equivalence of curved differential gradedalgebras, and for real-valued forms it factors through the usual Chen iteratedintegral.

Modeling bundle-valued forms on the path space with a curved iterated integral