# Volume 22 (2018) No. 1

## Volume 22 (2018) No. 1

### Hochschild homology and cohomology for involutive $A_\infty$-algebras

Ramsès Fernàndez-València

**Abstract:**

We present a study of the homological algebra of bimodules over $A_\infty$-algebras endowed with an involution. Furthermore we introduce a derived description of Hochschild homology and cohomology for involutive $A_\infty$-algebras.

### Baker-Gross theorem revisited

José Juan-Zacarías

**Abstract:**

F. Gross conjectured that any meromorphic solution of the Fermat Cubic $F_3 : x^3 + y^3 = 1$ are elliptic functions composed with entire functions. The conjecture was solved affirmatively first by I. N. Baker who found explicit formulas of those elliptic functions and later F. Gross gave another proof proving that in fact one of them uniformize the Fermat cubic. In this paper we give an alternative proof of the Baker and Gross theorems. With our method we obtain other analogous formulas. Some remarks on Fermat curves of higher degree is given.

### Non-contractible configuration spaces

Cesar A. Ipanaque Zapata

**Abstract:**

Let $F(M, k)$ be the configuration space of ordered $k$−tuples of distinct points in the manifold $M$. Using the Fadell-Neuwirth fibration, we prove that the configuration spaces $F(M, k)$ are never contractible, for $k \geq 2$. As applications of our results, we will calculate the LS category and topological complexity for its loop space and suspension.