Related papers: A variation on the homological nerve theorem
This note contains a newly streamlined version of the original proof that Outer space is contractible.
We describe explicitely the unique isomorphism $\mathrm{H}_{sin}^*(X,\underline{\mathbb{Z}})\xrightarrow{\sim} \check{\mathrm{H}}_{\mathcal{U}}^*(X,\underline{\mathbb{Z}})$ between the cohomologies computed with the singular and \v{C}ech…
A constructive version of the celebrated Boyle-Handelman theorem on the non-zero spectra of nonnegative matrices is presented.
We produce a new, shorter construction of a minor-universal planar graph.
We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.
We give a concise, conceptual proof of the universality of the relative Rezk nerve, due to Mazel-Gee.
In the last fifteen years a debate emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the…
This paper gives a slight refinement of a theorem of Hamilton, which shows that the velocity of a Keplerian motion moves on a circle.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
This is a research announcement of the theory of orbifold quantum cohomology.
We settle in the affirmative the Graham-Sloane conjecture.
We give a simple proof of a recently result concerning Hardy $q$-inequalities.
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We show that discrete and classical homotopy theories are equivalent after localizing at n-equivalences for any non-negative integer n. By constructing an explicit homotopy inverse to the graph nerve functor associating an n-fibrant cubical…
We prove a dualization of the Graham--Rothschild Theorem for variable words indexed by homogeneous trees.
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
We prove that seminormality of cut polytopes is equivalent to normality. This settles two conjectures regarding seminormality of cut polytopes.
We investigate to what extent persistent homology benefits from the properties of the usual homology theory.
A proposed solution to the Riemann Hypothesis
The paper presents an enriched categorical account of homological perturbation theory, including the formulation, proof and functoriality properties of the homological perturbation lemma.