Formal Contact Categories
Benjamin Cooper
TL;DR
This paper introduces a differential graded category associated with oriented surfaces, linking it to existing contact categories and enriching the algebraic framework for contact topology.
Contribution
It constructs a new differential graded category for surfaces that generalizes and relates to known contact categories in topology.
Findings
Homotopy category is triangulated.
Establishes connections with Honda's contact categories.
Relates to Tian's algebraic and Zarev's bordered sutured categories.
Abstract
To each oriented surface S, we associate a differential graded category Ko(S). The homotopy category Ho(Ko(S)) is a triangulated category which satisfies properties akin to those of the contact categories studied by K. Honda. These categories are also related to the algebraic contact categories of Y. Tian and to the bordered sutured categories of R. Zarev.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Algebraic Geometry and Number Theory