A primer on computational group homology and cohomology

These are expanded lecture notes of a series of expository talks surveying basic aspects of group cohomology and homology. They were written for someone who has had a first course in graduate algebra but no background in cohomology. You should know the definition of a (left) module over a (non-commutative) ring, what \zzz[G] is (where $G$ is a group written multiplicatively and \zzz denotes the integers), and some ring theory and group theory. However, an attempt has been made to (a) keep the presentation as simple as possible, (b) either provide an explicit reference of proof of everything. Several computer algebra packages are used to illustrate the computations, though for various reasons we have focused on the free, open source packages such as GAP and SAGE.Comment: 40+ pages. To appear in conference for the 60th birthday of Tont Gaglion

Nose gear steering system for vehicle with main skids Patent

Nose gear steering system for vehicles with main skids to provide directional stability after loss of aerodynamic contro

Pullback of parabolic bundles and covers of P1∖{0,1,∞}{\mathbb P}^1\setminus\{0,1,\infty\}

We work over an algebraically closed ground field of characteristic zero. A $G$-cover of ${\mathbb P}^1$ ramified at three points allows one to assign to each finite dimensional representation $V$ of $G$ a vector bundle $\oplus \mathscr{O}(s_i)$ on ${\mathbb P}^1$ with parabolic structure at the ramification points. This produces a tensor functor from representation of $G$ to vector bundles with parabolic structure that characterises the original cover. This work attempts to describe this tensor functor in terms of group theoretic data. More precisely, we construct a pullback functor on vector bundles with parabolic structure and describe the parabolic pullback of the previously described tensor functor.Comment: 25 page