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We describe how the graded minimal resolution of certain semigroup algebras is related to the combinatorics of some simplicial complexes. We obtain characterizations of the Cohen-Macaulay and Gorenstein conditions. The Cohen-Macaulay type is computed from combinatorics. As an application, we compute explicitly the graded minimal resolution of monomial both affine and simplicial projective surfaces.

Combinatorics of branchings in higher dimensional automata.

Gaucher, Philippe (2001)

Theory and Applications of Categories [electronic only]

Computation of cohomology operations on finite simplicial complexes.

González-Díaz, R., Real, P. (2003)

Homology, Homotopy and Applications

Conditions For A Realization Functor To Commute With Finite Products.

Carlos Ruiz Salguero, Roberto Ruis S. (1981)

Revista colombiana de matematicas

Construction géométrique des idempotents eulériens. Filtration des groupes de polytopes et des groupes d'homologie de Hochschild

F. Patras (1991)

Bulletin de la Société Mathématique de France

Continuous Alexander–Spanier cohomology classifies principal bundles with Abelian structure group

Bernd Günther, L. Mdzinarishvili (1997)

Fundamenta Mathematicae

We prove that Alexander-Spanier cohomology $H^{n} (X; G)$ with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.

Contractible simplicial objects

Michael Barr, John F. Kennison, Robert M. Raphael (2019)

Commentationes Mathematicae Universitatis Carolinae

We raise the question of when a simplicial object in a catetgory is deemed contractible. The literature offers three definitions. One is the existence of an “extra degeneracy”, indexed by $- 1$ , which does not quite live up to the name. This can be strengthened to a “strong extra degeneracy". Another possibility is that it be homotopic to a constant simplicial object. Despite claims in the literature to the contrary, we show that all three are distinct concepts with strong extra degeneracy implies extra...

Coxeter-like complexes.

Babson, Eric, Reiner, Victor (2004)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

Cubical sets and their site.

Grandis, Marco, Mauri, Luca (2003)

Theory and Applications of Categories [electronic only]

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