# Jacob LaubacherSt. Norbert College · Department of Mathematics

Jacob Laubacher

PhD

## About

16

Publications

1,509

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48

Citations

Citations since 2016

Introduction

Jacob Laubacher is an Associate Professor of Mathematics at St. Norbert College in De Pere, Wisconsin. Research is focused in homological algebra as well as group theory.

**Skills and Expertise**

## Publications

Publications (16)

We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the d-sphere for any \(d\ge 1\), we also investigate a deformation theory corresponding to the tertiary Hochschild cohomology, which naturally reduces to those studied for the secondary and usual H...

In this article, we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these graphs can or cannot occur as the prime character degree graph of a solvable group. An obvious expansion and gen...

In this article, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two notable exceptions) which members of the previously introduced graph family manifest as the prime character degree graph of some solvable group.

In this paper we study a generalization of K\"ahler differentials, which correspond to the secondary Hochschild homology associated to a triple $(A,B,\varepsilon)$. We establish computations in low dimension, while also showing how this connects with the kernel of a multiplication map.

In this paper, we continue the classification work done in the first paper of the same name. With careful modifications of our previous approach, we are able to deduce (with two notable exceptions) which members of the previously introduced graph family manifest as the prime character degree graph of some solvable group.

In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these graphs can or cannot occur as the prime character degree graph of a solvable group. An obvious expansion and genera...

We investigate prime character degree graphs of solvable groups. In particular, we consider a family of graphs $\Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion. In this paper we determine completely which graphs $\Gamma_{k,t}$ occur as the prime character degree graph of a solvable group.

We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve non-isomorphic connected graphs with six vertices, of which all except nine are classified in this paper. We also completely classify the disconnected graphs with six vertices.

We explore how the higher order Hochschild cohomology controls a deformation theory when the simplicial set models the 3-sphere. Besides generalizing to the $d$-sphere for any $d\geq1$, we also investigate a deformation theory corresponding to the tertiary Hochschild cohomology, which naturally reduces to those studied for the secondary and usual H...

In this paper we present a general construction that can be used to define the higher Hochschild homology for a noncommutative algebra. We also discuss other examples where this construction can be used.

Let G be a finite solvable group. We show that G does not have a normal nonabelian Sylow p-subgroup when its prime character degree graph ∆(G) satisfies a technical hypothesis.

In this paper we study the simplicial structure of the complex $C^{\bullet}((A,B,\varepsilon); M)$, associated to the secondary Hochschild cohomology. The main ingredient is the simplicial object $\mathcal{B}(A,B,\varepsilon)$, which plays a role equivalent to that of the bar resolution associated to an algebra. We also introduce the secondary cycl...

In this paper we study properties of the secondary Hochschild homology of the triple $(A,B,\varepsilon)$ with coefficients in $M$. We establish a type of Morita equivalence between two triples and show that $H_\bullet((A,B,\varepsilon);M)$ is invariant under this equivalence. We also prove the existence of an exact sequence which connects the usual...

In this paper we investigate the simplicial structure of a chain complex associated to the higher order Hochschild homology over the 3-sphere. We also introduce the tertiary Hochschild homology corresponding to a quintuple (A,B,C,ε,θ), which becomes natural after we organize the elements in a convenient manner. We establish these results by way of...