Simplicial Endomorphisms

[hal-00773001, v1] Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

Simplicial localization of monoidal structures, and a non-linear version of Deligne's conjecture

We show that if (M,⊗, I) is a monoidal model category then REnd M (I) is a (weak) 2-monoid in sSet. This applies in particular when M is the category of A-bimodules over a simplicial monoid A: the derived endomorphisms of A then form its Hochschild cohomology, which therefore becomes a simplicial 2-monoid.

Compact Endomorphisms of Certain Subalgebras of the Disk Algebra

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

Invariance of the barycentric subdivision of a simplicial complex

‎In this paper we prove that a simplicial complex is determined‎ ‎uniquely up to isomorphism by its barycentric subdivision as well as‎ ‎its comparability graph‎. ‎We also put together several algebraic‎, ‎combinatorial and topological invariants of simplicial complexes‎.