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2018 Relative $2$–Segal spaces
Matthew B Young
Algebr. Geom. Topol. 18(2): 975-1039 (2018). DOI: 10.2140/agt.2018.18.975

Abstract

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 –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.

Citation

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Matthew B Young. "Relative $2$–Segal spaces." Algebr. Geom. Topol. 18 (2) 975 - 1039, 2018. https://doi.org/10.2140/agt.2018.18.975

Information

Received: 8 February 2017; Revised: 7 October 2017; Accepted: 30 October 2017; Published: 2018
First available in Project Euclid: 22 March 2018

zbMATH: 06859611
MathSciNet: MR3773745
Digital Object Identifier: 10.2140/agt.2018.18.975

Subjects:
Primary: 18G30
Secondary: 16G20, 18G55, 19G38

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 2 • 2018
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