Geodesic
Relative 2–Segal spaces
Young, Matthew1
1 The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 975-1039

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We introduce a relative version of the 2–Segal simplicial spaces defined by Dyckerhoff and Kapranov, and Gálvez-Carrillo, Kock and Tonks. Examples of relative 2–Segal spaces include the categorified unoriented cyclic nerve, real pseudoholomorphic polygons in almost complex manifolds and the ℛ∙ –construction from Grothendieck–Witt theory. We show that a relative 2–Segal space defines a categorical representation of the Hall algebra associated to the base 2–Segal space. In this way, after decategorification we recover a number of known constructions of Hall algebra representations. We also describe some higher categorical interpretations of relative 2–Segal spaces.

DOI : 10.2140/agt.2018.18.975
Classification : 18G30, 18G55, 16G20, 19G38
Keywords: higher Segal spaces, categorified Hall algebra representations, categories with duality, Grothendieck-Witt theory

Young, Matthew 1

1 The Institute of Mathematical Sciences and Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong 
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Young, Matthew. Relative 2–Segal spaces. Algebraic and Geometric Topology, Tome 18 (2018) no. 2, pp. 975-1039. doi: 10.2140/agt.2018.18.975

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