Much like a medical graft operation, Dehn surgery uses mathematical scalpels to slice topological features from an object and stitch new features to their raw edges.

poplar pruning

For instance, in a pair of shears, we can cut a hole through each individual shank and fasten a pivot screw such that the new, single shape has two holes.

my fingers grasp

In some cases, surgery creates the holes themselves when an object is sewn back to itself rather than another object.

hawk moth nibbles
dot a leaf

Of course, some holes last longer than others.

another empty
bottle

Homotopy quantifies the number of holes in an object by winding around that object to ascertain if the mathematical string can be pulled back to its origin point.

its silk strand
a wound blanket
sudden puncture

Qualitatively, even the most meandering path can contract to its origin point if the holes are surgically filled.

the long
trudge
to rehab

—Tied for Third Place Winner of MacQ’s Cheribun Challenge #4

—This issue also features an essay by Farrelly which includes her analyses of the 97 cheribun published in MacQ from January 2022 through June 2026: Cheribun: A Craft Perspective

Publisher’s Note:

A definition for fellow laypersons: In topology, a branch of mathematics that studies shapes and spaces, Dehn surgery is a “cut and paste” technique used to build and study three-dimensional (3D) shapes by cutting and twisting knots. Imagine this “drill and fill”: cut a long tube of dough from a solid sphere (aka “donut”); twist the ends like a corkscrew (which creates a Möbius effect); and use the knotted tube to patch the “donut” hole, thus creating a new 3D shape. Dehn surgery has practical applications in quantum computing, materials science, and robotics, among others.

All of this pretty much boggles my mind!

And yet I can imagine a couple of literary applications, too. First, “drill and fill”: Treat a clunky metaphor or problematic stanza or paragraph as the “knot”; cut the lines or phrases out and shift their emotional center; and stitch them back together with a thematic twist.

Second, the Möbius effect as applied to linear storytelling: Instead of the usual 1-2-3 plot structure, extract a single emotional memory, twist its chronology, and patch it back into the piece to create a looping narrative (for example, a pantoum).

Bio: Colleen M. Farrelly