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On several varieties of cacti and their relations.

Kaufmann, Ralph M. (2005)

Algebraic & Geometric Topology

On the loop homology of complex projective spaces

David Chataur, Jean-François Le Borgne (2011)

Bulletin de la Société Mathématique de France

In this short note we compute the Chas-Sullivan BV-algebra structure on the singular homology of the free loop space of complex projective spaces. We compare this result with computations in Hochschild cohomology.

Open/Closed string topology and moduli space actions via open/closed Hochschild actions.

Kaufmann, Ralph M. (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Operads for $n$ -ary algebras – calculations and conjectures

Martin Markl, Elisabeth Remm (2011)

Archivum Mathematicum

In [8] we studied Koszulity of a family ${t 𝒜 𝑠𝑠}_{d}^{n}$ of operads depending on a natural number $n \in ℕ$ and on the degree $d \in ℤ$ of the generating operation. While we proved that, for $n \leq 7$ , the operad ${t 𝒜 𝑠𝑠}_{d}^{n}$ is Koszul if and only if $d$ is even, and while it follows from [4] that ${t 𝒜 𝑠𝑠}_{d}^{n}$ is Koszul for $d$ even and arbitrary $n$ , the (non)Koszulity of ${t 𝒜 𝑠𝑠}_{d}^{n}$ for $d$ odd and $n \geq 8$ remains an open problem. In this note we describe some related numerical experiments, and formulate a conjecture suggested by the results of these computations.

Operads in iterated monoidal categories.

Forcey, Stefan, Siehler, Jacob, Sowers, E.Seth (2007)

Journal of Homotopy and Related Structures

Operády v současné matematice

Martin Markl (2003)

Pokroky matematiky, fyziky a astronomie