Doubly slice knots and metabelian obstructions

An n-dimensional knot Sn⊂Sn+2 is called doubly slice if it occurs as the cross section of some unknotted (n+1)-dimensional knot. For every n it is unknown which knots are doubly slice, and this remains one of the biggest unsolved problems in high-dimensional knot theory. For ℓ>1, we use signatures coming from L(2)-cohomology to develop new obstructions for (4ℓ−3)-dimensional knots with metabelian knot groups to be doubly slice. For each ℓ>1, we construct an infinite family of knots on which our obstructions are nonzero, but for which double sliceness is not obstructed by any previously known invariant

Guide to the Dr. L.S. Dederick Papers, 1908-1956, undated

Louis Serle (L.S.) Dederick was born in Chicago in 1883. He received his Ph.D. in Mathematics from Harvard University in 1909. From 1909 – 1917 he was a professor at Princeton University. From 1917 – 1924 he was professor at the U.S. Naval Academy in Annapolis, Maryland. In 1926 Dederick began working for the U.S. Army, Ordnance. During his time there he was the Associate Director of the Ballistic Research Laboratory at the Aberdeen Proving Grounds in Aberdeen, Maryland where he focused on ballistics research. While Dederick worked as a mathematician at the Aberdeen Proving Grounds, he was involved with numerous projects. He worked in the fields of ballistics calculations, the development of computing methods for machines which included differential analyzers, the Bell Relay computer, oversaw the creation of the ENIAC computer (the world’s first digital computer), as well as its successors the EDVAC computer and the ORDVAC computer. These computers were designed with the goal of making ballistics calculations more quickly and efficiently. Some of his work on these projects included project management, administrative work, and search for personnel to add to project teams. His immediate supervisors while working at Aberdeen included Col. Leslie E. Simon and Col. Alden P. Taber. Dederick retired from this position in May 1953. After his retirement he was pulled into efforts of the House of Un-American Activities Committee (HUAC) in 1954 to give statements on behalf of some of the workers he supervised who were being questioned about possible connections to communism. Dederick passed away in 1972. He is buried in Princeton Cemetery, located in Princeton, NJ. This Collection consists mostly of documents from L.S. Dederick’s time at Aberdeen Proving Ground in Aberdeen, Maryland. This Includes his work with the Electronic Numerical Integrator And Computer, better known as the ENIAC, the world’s first digital computer, as well as the Electronic Discrete Variable Automatic Computer, known as the EDVAC. The ENIAC, completed in 1945, aided in allowing the United States Army’s Ballistic Research Laboratory to more easily perform ballistics calculations. It marks the beginning of the computer age

A Khovanov stable homotopy type for colored links

We extend Lipshitz-Sarkar's definition of a stable homotopy type associated to a link L whose cohomology recovers the Khovanov cohomology of L. Given an assignment c (called a coloring) of positive integer to each component of a link L, we define a stable homotopy type X_col(L_c) whose cohomology recovers the c-colored Khovanov cohomology of L. This goes via Rozansky's definition of a categorified Jones-Wenzl projector P_n as an infinite torus braid on n strands. We then observe that Cooper-Krushkal's explicit definition of P_2 also gives rise to stable homotopy types of colored links (using the restricted palette {1, 2}), and we show that these coincide with X_col. We use this equivalence to compute the stable homotopy type of the (2,1)-colored Hopf link and the 2-colored trefoil. Finally, we discuss the Cooper-Krushkal projector P_3 and make a conjecture of X_col(U_3) for U the unknot

A calculus for flow categories

We describe a calculus of moves for modifying a framed flow category without changing the associated stable homotopy type. We use this calculus to show that if two framed flow categories give rise to the same stable homotopy type of homological width at most three, then the flow categories are move equivalent. The process we describe is essentially algorithmic and can often be performed by hand, without the aid of a computer program