The study of cohomology dwells in a glasshouse,
Where the sun kisses the sheaves, leaving its sections glistening in dew,
Where the stalks, step out from their germs, silently but surely,
bearing a fruitful spectrum of rings, ideals and modules, just to name a few.
The complexes delve into the darkened soil
And run off to infinity, lest they be acyclic, soft or fine.
With their coboundary operators, like vessels, weaving in between,
Forming an intricate tapestry; a certain geometric richness captured in its vines.
Cohomology, like the botanical living, come in various types,
Singular grow from standard simplexes and simplicial, from polygons,
Cech built upon open coverings, laid out with meticulous care,
While De Rham and Dolbeault sprout from dancing differential forms.
Invariant and unmoved by rueful wind or bleak winter snow,
each tells a unique and beautiful story about the geometry of a space,
and yet, somehow they are all connected by some mysterious force,
and sit at the topological, differential and holomorphic worlds’ interface.
Therein lies an air of enigma in cohomology,
one, enchanting and sacred, esoteric and abstract,
So bury my bones among the chains, cochains and resolutions,
So that my soul can live on through sequences of long and short exact.