arXiv subjects

Esma Dirican Erdal

Publications and source records attributed to Esma Dirican Erdal.

7 recordsLinked to original sources

arXiv2026

On twisted torsion of compact $3$-manifolds

In this paper, we examine the behavior of twisted Reidemeister torsion for compact, connected, oriented $3$-manifolds under the connected sum operation. Under appropriate assumptions, we establish a multiplicative relation for the torsion associated with representations into a complex reductive algebraic group. Our results are consistent with the known behavior of torsion-type invariants and provide a formulation that may be useful for further investigations of decomposition properties in $3$-manifold topology.

math.GT↗

arXiv2026

The Supertrace Defect of a Graded Endomorphism

Motivated by Igusa's relation between relative cyclic homology and the logarithm of the graded Cartan determinant, we isolate the homological step behind the passage from logarithmic determinants to traces of powers. For a bounded chain complex $(C_*,d)$ and a degree-zero graded endomorphism $f$, not assumed to commute with $d$, we construct the universal quotient on which $f$ becomes a chain map. The kernel of this reflection iterates to a canonical functorial minimal filtration, whose Rees module gives a flat degeneration to an uncurved associated graded. For finite-dimensional chain groups all power supertraces of $f$ are represented by Lefschetz traces on this associated graded, so the resulting logarithmic-determinant and zeta series admit a canonical homological representation.

math.AG↗

arXiv2026

Multiplicativity of Reidemister-Franz Torsion for Even Manifolds

We study Reidemeister-Franz torsion for non-acyclic cellular chain complexes arising from closed, oriented, highly connected even dimensional manifolds. The monoid of such manifolds under connected sum admits a unique factorisation into indecomposable elements. Using this factorisation, we prove that the Reidemeister-Franz torsion of an even-dimensional manifold decomposes multiplicatively as the product of the torsions of its prime factors without any corrective term.

math.AT↗

arXiv2024

Higher Analogues of Discrete Topological Complexity

In this paper, we introduce the n-th discrete topological complexity and study its properties such as its relation with simplicial Lusternik-Schnirelmann category and how the higher dimensions of discrete topological complexity relate with each other. Moreover, we find a lower bound of $n-$discrete topological complexity which is given by the n-th usual topological complexity of the geometric realisation of that complex. Furthermore, we give an example for the strict case of that lower bound.

math.AT↗

arXiv2022

The Adjoint Reidemeister Torsion for Compact 3-Manifolds Admit a Unique Decomposition

Let $M$ be a triangulated, oriented, connected compact $3$-manifold with connected non-empty boundary. Such a manifold admits a unique decomposition into $\triangle$-prime $3$-manifolds. In this paper, we show that the adjoint Reidemeister torsion has a multiplicative property on the disk sum decomposition of compact $3$-manifolds without a corrective term.

math.GT↗

arXiv2022

Gluing Formulas for Volume Forms on Representation Varieties of Surfaces

Let $Σ_{g,n}$ be a compact oriented surface with genus $g\geq 2$ bordered by $n$ circles. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah-Bott-Goldman-Narasimhan symplectic form on the space of representations of $π_1(Σ_{g,0})$ in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of $Σ_{g,0}$ in terms of torsions of $Σ_{2,2},$ $Σ_{2,1},$ and boundary circles $\mathbb{S}^1.$ Then, by using Heusener and Porti's results on $Σ_{g,n},$ we show that the symplectic volume form on the representation variety of $Σ_{g,0}$ can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces $Σ_{2,1}$ and $Σ_{2,2}.$

math.AT↗

arXiv2021

Reidemeister-Franz Torsion of Compact Orientable Surfaces via Pants Decomposition

Let $Σ_{g,n}$ denote the compact orientable surface with genus $g\geq 2$ and boundary disjoint union of $n$ circles. By using a particular pants-decomposition of $Σ_{g,n},$ we obtain a formula that computes the Reidemeister torsion of $Σ_{g,n}$ in terms of Reidemeister torsions of pairs of pants.

math.GT↗