Abstract:
In this paper we will study deformations of A-infinity algebras. We will also answer questions relating to Moore algebras which are one of the simplest nontrivial examples of an A-infinity algebra. We will compute the Hochschild cohomology of odd Moore algebras and classify them up to a unital weak equivalence. We will construct miniversal deformations of particular Moore algebras and relate them to the universal odd and even Moore algebras. Finally we will conclude with an investigation of formal one-parameter deformations of an A-infinity algebra.

Abstract:
We embed the category of Moore spectra as a full subcategory of an abelian category, and make some remarks about abelian embeddings of various other categories of spectra.

Abstract:
In this (mostly expository) paper, we review a proof of the following old theorem of R.L. Moore: for a closed equivalence relation on the 2-sphere such that all equivalence classes are connected and non-separating, and not all points are equivalent, the quotient space is homeomorphic to the 2-sphere. The proof uses a general topological theory close to but simpler than an original theory of Moore. The exposition is organized so that to make applications of Moore's theory (not only Moore's theorem) in complex dynamics easier, although no dynamical applications are mentioned here.

Abstract:
We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs.

Abstract:
The analytical requirements of Moore in ethical questions are so high that we labour under the impression that all morals and ethics before (and even after) he wrote the Principia, fall into the delusion he calls "naturalistic". It may be granted that to do one’s duty, to realize one’s person, to follow a particular intuition etc.. is to do good ; but why would the good consist in doing one’s duty, realizing one’s person and conforming to a particular affect ? It is difficult to see how Utilitarianism would allow to resolve the "inverse problem" ; yet Moore claims himself to be a Utilitarian and inscribes his purpose in the wake of Bentham’s, Stuart Mill’s and Sidgwick’s. How is it possible? Of course, there are many sorts of Utilitarianism. What did Moore want? Did he want, at the beginning of the twentieth century, to add another sort of utilitarianism to a long list of ramifications and branching? What meaning should we give his ideal utilitarianism, as he called and promoted it in Principia Ethica?

Abstract:
The analytical requirements of Moore in ethical questions are so high that we labour under the impression that all morals and ethics before (and even after) he wrote the Principia, fall into the delusion he calls "naturalistic". It may be granted that to do one’s duty, to realize one’s person, to follow a particular intuition etc.. is to do good ; but why would the good consist in doing one’s duty, realizing one’s person and conforming to a particular affect ? It is difficult to see how Utilitarianism would allow to resolve the "inverse problem" ; yet Moore claims himself to be a Utilitarian and inscribes his purpose in the wake of Bentham’s, Stuart Mill’s and Sidgwick’s. How is it possible? Of course, there are many sorts of Utilitarianism. What did Moore want? Did he want, at the beginning of the twentieth century, to add another sort of utilitarianism to a long list of ramifications and branching? What meaning should we give his ideal utilitarianism, as he called and promoted it in Principia Ethica?

Abstract:
Let G be a connected and simply connected two-step nilpotent Lie group and Γ a lattice subgroup of G. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition of the quasi-regular representation Ind_Γ^G(1). Extending then the Abelian case.

Abstract:
Let $G$ be a connected and simply connected two-step nilpotent Lie group and $\Gamma$ a lattice subgroup of $G$. In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition of the quasi-regular representation ${\rm Ind}_{\Gamma}^G(1)$. Extending then the Abelian case.

Abstract:
We suggest a new generalization of Pontryagin duality from the category of Abelian locally compact groups to a category which includes all Moore groups, i.e. groups whose irreducible representations are finite-dimensional. Objects in this category are pro-C*-algebras with a structure of Hopf algebras (in the strict algebraic sense) with respect to a certain topological tensor product.