Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Algebraic Topology

arXiv:1812.07604 (math)
[Submitted on 18 Dec 2018]

Title:The Topological Complexity of Finite Models of Spheres

Authors:Shelley Kandola
View PDF
Abstract:In this paper, we examine how topological complexity, simplicial complexity, discrete topological complexity, and combinatorial complexity compare when applied to models of $S^1$. We prove that the topological complexity of non-minimal finite models of $S^1$ can be less-than-or-equal-to 3, and that the TC of the minimal finite model of any $n$-sphere is equal to 4 for $n \geq 1$. We show the former using properties of the LS-category, and we show the latter by proving that the TC of the non-Hausdorff suspension of any finite connected $T_0$ space is equal to 4. We also prove a result about the topological complexity of non-Hausdorff joins of discrete finite spaces, allowing us to exhibit spaces weakly homotopy equivalent to a wedge of circles with arbitrarily high TC.
Comments: 10 pages, 1 figure
Subjects: Algebraic Topology (math.AT)
Cite as: arXiv:1812.07604 [math.AT]
  (or arXiv:1812.07604v1 [math.AT] for this version)
  https://doi.org/10.48550/arXiv.1812.07604

Submission history

From: Shelley Kandola [view email]
[v1] Tue, 18 Dec 2018 19:15:26 UTC (11 KB)
Full-text links:

Access Paper:

view license
Current browse context:
math.AT
< prev   |   next >
new | recent | 2018-12
Change to browse by:
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)