Blowdown, $k$-wedge and evenness of quasitoric orbifolds

TL;DR

This paper introduces new geometric constructions called $k$-wedge and blowdown for simple polytopes and quasitoric orbifolds, analyzing their effects on cohomology and providing infinitely many new examples.

Contribution

It develops the polytopal $k$-wedge and blowdown constructions for simple polytopes and quasitoric orbifolds, expanding the class of known examples and analyzing their cohomological properties.

Findings

$k$-wedge and blowdown constructions alter the retraction sequences.

These constructions produce infinitely many new quasitoric orbifolds.

The torsion in cohomology is compared before and after the constructions.

Abstract

In this paper, we introduce polytopal $k$-wedge construction and blowdown of a simple polytope and inspect the effect on the retraction sequence of a simple polytope due to $k$-wedge construction and blowdown. In relation to this construction, we introduce the $k$-wedge and blowdown of a quasitoric orbifold. We compare the torsions in the integral cohomologies of $k$-wedges and blowdowns of a quasitoric orbifold with the original one. These two constructions provide infinitely many integrally equivariantly formal quasitoric orbifolds from a given one.