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A case study in Interaction cohomology Oliver Knill 3182016 Simplicial Cohomology Simplicial cohomology is defined by an exterior derivative dF x = F dx on valuation forms…
THE STRONG RING OF SIMPLICIAL COMPLEXES OLIVER KNILL Abstract The strong ring R is a commutative ring generated by finite abstract simplicial complexes To every G ∈ R be-…
POINCARÉ HOPF FOR VECTOR FIELDS ON GRAPHS OLIVER KNILL Abstract. We generalize the Poincaré-Hopf theorem ∑ v iv = χG to vector fields on a finite simple graph Γ =…
THE MCKEAN-SINGER FORMULA IN GRAPH THEORY OLIVER KNILL Abstract For any finite simple graphG = VE the discrete Dirac operator D = d+d∗ and the Laplace-Beltrami operator…
ON A DEHN-SOMMERVILLE FUNCTIONAL FOR SIMPLICIAL COMPLEXES OLIVER KNILL Abstract. Assume G is a finite abstract simplicial complex with f -vector (v0, v1, . . . ), and generating…
A GRAPH THEORETICAL POINCARÉ-HOPF THEOREM OLIVER KNILL Abstract. We introduce the index i(v) = 1 − χ(S−(v)) for critical points of a locally injective function f on…
CHARACTERISTIC LENGTH AND CLUSTERING OLIVER KNILL Abstract We explore relations between various variational prob- lems for graphs: among the functionals considered are Euler…
CURVATURE FROM GRAPH COLORINGS OLIVER KNILL Abstract. Given a finite simple graphG = V,E with chromatic number c and chromatic polynomial Cx. Every vertex graph col- oring…
AN ELEMENTARY DYADIC RIEMANN HYPOTHESIS OLIVER KNILL Abstract. The connection zeta function of a finite abstract sim- plicial complex G is defined as ζLs = ∑ x∈G λ…
CURVATURE FROM GRAPH COLORINGS OLIVER KNILL Abstract Given a finite simple graphG = VE with chromatic number c and chromatic polynomial Cx Every vertex graph col- oring f…
A GRAPH THEORETICAL POINCARÉ-HOPF THEOREM OLIVER KNILL Abstract We introduce the index iv = 1 − χS−v for critical points of a locally injective function f on the vertex…
THE MCKEAN-SINGER FORMULA IN GRAPH THEORY OLIVER KNILL Abstract. For any finite simple graphG = V,E, the discrete Dirac operator D = d+d∗ and the Laplace-Beltrami operator…
COMPLEXES, GRAPHS, HOMOTOPY, PRODUCTS AND SHANNON CAPACITY OLIVER KNILL Abstract. A finite abstract simplicial complex G defines the Barycentric re- finement graph φG =…
THE STRONG RING OF SIMPLICIAL COMPLEXES OLIVER KNILL Abstract The strong ring R is a commutative ring generated by finite abstract simplicial complexes To every G ∈ R be-…
doi.10.1112/10.1112/S00246107..0....?Journal of Topology 5 (2012) 977–1010 C2012 London Mathematical Society doi:10.1112/jtopol/jts026 Stable complexity and simplicial
Computational Algebraic Topology Hilary Term 2012 1 1. Simplicial complexes 1.1. Definitions An abstract, finite simplicial complex K is a collection of non-empty subsets…
ON A DEHN-SOMMERVILLE FUNCTIONAL FOR SIMPLICIAL COMPLEXES OLIVER KNILL Abstract Assume G is a finite abstract simplicial complex with f -vector v0 v1 and generating function…
Simplicial Complexes Jean-Daniel Boissonnat Geometrica, INRIA http://www-sop.inria.fr/geometrica Algorithmic Geometry Triangulations 1 Simplicial Complexes 1 / 1 http://www-sop.inria.fr/geometrica…
THE LOCAL h-VECTOR OF THE CLUSTER SUBDIVISION OF A SIMPLEX CHRISTOS A ATHANASIADIS AND CHRISTINA SAVVIDOU Abstract The cluster complex ∆Φ is an abstract simplicial complex…
THE SIMPLICIAL EHP SEQUENCE IN A1–ALGEBRAIC TOPOLOGY KIRSTEN WICKELGREN AND BEN WILLIAMS ABSTRACT We give a tool for understanding simplicial desuspension in A1-algebraic…