ORCID

https://orcid.org/0009-0000-7562-6655

Date of Award

Spring 2026

Language

English

Embargo Period

5-16-2026

Document Type

Master's Thesis

Degree Name

Master of Arts (MA)

College/School/Department

Department of Mathematics and Statistics

Program

Mathematics

First Advisor

Marco Varisco

Committee Members

Marco Varisco, Brenda Johnson, Antun Milas

Keywords

Assembly Maps, Global Orbit Category, Higher Category Theory, Equivariant Homotopy Theory

Subject Categories

Geometry and Topology

Abstract

We reformulate the foundations of assembly maps in the context of the global orbit ∞-category of all discrete groups. We first show that the ∞-categorical slice of the global orbit ∞-category over any fixed group G is equivalent to the orbit 1-category of G, and we also frame the subgroup 1-category of G in this global context. We then use the afore-mentioned equivalence to redefine assembly maps as counits of the adjunction between left Kan extension and restriction, and give purely ∞-categorical and conceptual proofs of known results, such as the Transitivity Principle. Additionally, we give equivalent formulations for what it means for a functor defined out of the global orbit ∞-category to satisfy an isomorphism conjecture, and we show how well-studied examples, such as the Farrell–Jones Conjecture, fit into this global framework.

License

This work is licensed under the University at Albany Standard Author Agreement.

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