| Title: | Vertex numbers of simplicial complexes with free abelian fundamental group |
|---|
| Authors: | ID Frick, Florian (Author)
ID Superdock, Matt (Author) |
|---|
| Files: |  AMC_Superdock,Frick_2025.pdf (401,27 KB)
MD5: FB1AE621997DB2C459DC14E1E76E80B2
 https://amc-journal.eu/index.php/amc/article/view/3089
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | FAMNIT - Faculty of Mathematics, Science and Information Technologies
ZUP - University of Primorska Press
|
|---|
| Abstract: | We show that the minimum number of vertices of a simplicial complex with fundamental group ℤn is at most O(n) and at least Ω(n3/4). For the upper bound, we use a result on orthogonal 1-factorizations of K2n. For the lower bound, we use a fractional Sylvester–Gallai result. This application of extremal results in discrete geometry seems to be new. We also prove that any group presentation ⟨S|R⟩ ≅ ℤn whose relations are of the form gahbic for g, h, i ∈ S has at least Ω(n3/2) generators. |
|---|
| Keywords: | simplicial complex, fundamental group, incidence geometry |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 13.02.2025 |
|---|
| Publisher: | Založba Univerze na Primorskem |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 16 str. |
|---|
| Numbering: | Vol. 25, no. 1, [article no.] P1.05 |
|---|
| PID: | 20.500.12556/RUP-21770  |
|---|
| UDC: | 51 |
|---|
| eISSN: | 1855-3974 |
|---|
| DOI: | 10.26493/1855-3974.3089.b49 |
|---|
| Publication date in RUP: | 18.09.2025 |
|---|
| Views: | 441 |
|---|
| Downloads: | 5 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
