Date of Submission

Spring 2023

Academic Program

Mathematics

Project Advisor 1

Ethan Bloch

Abstract/Artist's Statement

Stellate neighborhoods are created by gluing half disks together along their straight edges. A 1-stellate neighborhood is a half disk, a 2-stellate neighborhood is a disk, a 3-stellate neighborhood is 3 half disks glued together to make a star-like shape, and so on. For a topological space $X$, and for each $n \in \nn$, the $n$-stellate subspace of $X$ is the set of all points in $X$ that have a neighborhood homeomorphic to an $n$-stellate neighborhood. I will be examining topological spaces called stellate unions, where each point in the space is contained in an $n$-stellate subspace for some $n \in \nn$. All surfaces and surfaces with boundary are stellate unions, yet there are many stellate unions that are not surfaces or surfaces with boundary. I will explore some stellate unions called extended graph twists and examine their orientability.

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Open Access

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