When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics. Its Hochschild cohomology predicts var...

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered.

In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold and prove they converge to their differential-geometric analogues as the triangulation becomes small. The first such result is for a cochain cup product converging to the wedge product on differential forms. Moreover, we show any extension of this product to a C∞algebra also converges to ...

Transforming a matrix over a field to echelon form, or decomposing the matrix as a product of structured matrices that reveal the rank profile, is a fundamental building block of computational exact linear algebra. This paper surveys the well known variations of such decompositions and transformations that have been proposed in the literature. We present an algorithm to compute the CUP decompos...

We construct a cubical CW-complex CK(M3) whose rational cohomology algebra contains Vassiliev invariants of knots in the 3-manifold M3. We construct CK(R3) by attaching cells to CK(R3) for every degenerate 1-singular and 2-singular knot, and we show that π1(CK(R 3)) = 1 and π2(CK(R 3)) = Z. We give conditions for Vassiliev invariants to be nontrivial in cohomology. In particular, for R3 we show...

In an earlier paper we have shown that the pair-of-pants product on the Floer homology of the cotangent bundle of an oriented compact manifold Q corresponds to the Chas-Sullivan loop product on the singular homology of the free loop space of Q. We now give chain level constructions of further product structures in Floer homology, corresponding to the cup product on the homology of any path spac...

We estimate the role of peer effects in technology adoption using data from a randomized distribution of menstrual cups in Nepal. Using individual randomization, we estimate causal effects of peer exposure on adoption. We find strong evidence of peer effects: two months after distribution, one additional friend with access to the menstrual cup increases usage by 18.6 percentage points. Using th...