# Quadratic heptagon cohomology

@inproceedings{Korepanov2021QuadraticHC, title={Quadratic heptagon cohomology}, author={Igor G. Korepanov}, year={2021} }

A cohomology theory is proposed for the recently discovered heptagon relation—an algebraic imitation of a 5-dimensional Pachner move 4–3. In particular, ‘quadratic cohomology’ is introduced, and it is shown that it is quite nontrivial, and even more so if compare heptagon with either its higher analogues, such as enneagon or hendecagon, or its lower analogue, pentagon. Explicit expressions for the nontrivial quadratic heptagon cocycles are found in dimensions 4 and 5.

## References

SHOWING 1-10 OF 10 REFERENCES

Nonconstant hexagon relations and their cohomology

- Mathematics
- 2018

A construction of hexagon relations—algebraic realizations of four-dimensional Pachner moves—is proposed. It goes in terms of “permitted colorings” of 3-faces of pentachora (4-simplices), and its…

Hexagon cohomologies and polynomial TQFT actions

- Mathematics, Physics
- 2017

Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call…

Simplicial moves on complexes and manifolds

- Mathematics
- 1999

Here are versions of the proofs of two classic theorems of combinatorial topology. The first is the result that piecewise linearly homeomorphic simplicial complexes are related by stellar moves. This…

Exact solutions and mixing in an algebraic dynamical system

- Mathematics
- 2005

AbstractLet
$$\mathcal{A}$$
be an n×n matrix with entries aij in the field ℂ. We consider two involutive operations on these matrices: the matrix inverse I:
$$\mathcal{A}$$
↦
$$\mathcal{A}$$
−1…

Heptagon relation in a direct sum

- Mathematics
- 2020

An ansatz is proposed for heptagon relation, that is, algebraic imitation of five-dimensional Pachner move 4--3. Our relation is realized in terms of matrices acting in a direct sum of…

Grassmannian-parameterized solutions to direct-sum polygon and simplex equations

- Mathematics, Physics
- 2020

We consider polygon and simplex equations, of which the simplest nontrivial examples are pentagon (5-gon) and Yang--Baxter (2-simplex), respectively. We examine the general structure of (2n+1)-gon…

Müller-Hoissen, Simplex and polygon equations, SIGMA

- 2015

PL homeomorphic manifolds are equivalent by elementary shellings

- Europ. J. Combinatorics
- 1991

homeomorphic manifolds are equivalent by elementary shellings

- Europ. J. Combinatorics
- 1991