arXiv subjects

Zoran Petrić

Publications and source records attributed to Zoran Petrić.

2 recordsLinked to original sources

arXiv2025

Restricted (2+1)-TQFTs supported by thickened and solid tori

A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants.

math.GT↗

arXiv2017

The $n$-fold reduced bar construction

This paper is about a correspondence between monoidal structures in categories and $n$-fold loop spaces. We develop a new syntactical technique whose role is to substitute the coherence results, which were the main ingredients in the proofs that the Segal-Thomason bar construction provides an appropriate simplicial space. The results we present here enable more common categories to enter this delooping machine. For example, such is the category of finite sets with two monoidal structures brought by the disjoint union and Cartesian product.

math.CT↗