Reidemeister-Franz torsion as a homomorphism
| dc.authorid | 0000-0003-1223-3007 | |
| dc.contributor.author | Dirican Erdal, Esma | en_US |
| dc.contributor.editor | Zeren, Yusuf | en_US |
| dc.contributor.editor | Kirişci, Murat | en_US |
| dc.contributor.editor | Çevikel, Adem Cengiz | en_US |
| dc.date.accessioned | 2026-03-16T08:05:56Z | |
| dc.date.available | 2026-03-16T08:05:56Z | |
| dc.date.issued | 2025-05-09 | |
| dc.department | Işık Üniversitesi, Mühendislik ve Doğa Bilimleri Fakültesi, Matematik Bölümü | en_US |
| dc.department | Işık University, Faculty of Engineering and Natural Sciences, Department of Mathematics | en_US |
| dc.description | This work was partially supported by TÜBİTAK under the project number 124F247. | en_US |
| dc.description.abstract | Let us denote the Diff-isomorphism classes of n-dimensional non-empty, closed, connected, oriented differentiable manifolds by Mn Diff. An n-manifold Mn is called highly connected if π1(Mn)=0 for i=0,…, ⌊n/2⌋-1. So the Diff-isomorphism classes of n-dimensional highly connected differentiable manifolds is given as MnDiff,hc= {Mn𝜖 MDiff | Mn is highly con-nected}. Hence by [1], MnDiff and MnDiff,hc are abelian monoids under the connected sum. By [1]-[3], the monoid M2nDiff,hc is a unique factorisation monoid provided that n ≡ 3,5,7 mod 8 except for n=15 or n=31. Suppose that W2n 𝜖 M2nDiff,hc .Then W2n admits a unique connected sum decomposition into 2n-manifolds that can not be decomposed any further, W2n=M1#M2#⋯#Mj. By using such a connected sum decomposition, we prove that Rei- demeister-Franz torsion can be seen as a monoid homomorphism |T RF − |: M2nDiff,hc → R+given by | T RF (W2n)| = | T RF (M1)| x |T RF (M2)| x ⋯ x | T RF (Mj)|. | en_US |
| dc.description.version | Publisher's Version | en_US |
| dc.identifier.citation | Dirican Erdal, E. (2025). Reidemeister-Franz torsion as a homomorphism. Paper presented at the 8th International HYBRID Conference on Mathematical Advances and Applications, 48-48. | en_US |
| dc.identifier.endpage | 48 | |
| dc.identifier.isbn | 9786056938771 | |
| dc.identifier.startpage | 48 | |
| dc.identifier.uri | https://hdl.handle.net/11729/7135 | |
| dc.identifier.uri | https://2025.icomaas.com/ | |
| dc.institutionauthor | Dirican Erdal, Esma | en_US |
| dc.institutionauthorid | 0000-0003-1223-3007 | |
| dc.language.iso | en | en_US |
| dc.peerreviewed | Yes | en_US |
| dc.publicationstatus | Published | en_US |
| dc.publisher | Yıldız Teknik Üniversitesi | en_US |
| dc.relation.ispartof | 8th International HYBRID Conference on Mathematical Advances and Applications | en_US |
| dc.relation.publicationcategory | Konferans Öğesi - Uluslararası - Başka Kurum Yazarı | en_US |
| dc.rights | info:eu-repo/semantics/openAccess | en_US |
| dc.subject | Reidemeister-Franz torsion | en_US |
| dc.subject | Unique factorization monoid | en_US |
| dc.subject | Differentiable manifolds | en_US |
| dc.title | Reidemeister-Franz torsion as a homomorphism | en_US |
| dc.type | Conference Object | en_US |
| dspace.entity.type | Publication | en_US |
