Fruit Belt Neighborhood Asset Inventory

The Fruit Belt is bordered by North Street on the north, Jefferson Street on the east, the Kensington Expressway on the south, and Michigan Street on the west. The Buffalo Niagara Medical Campus (BNMC) lies directly west of the Fruit Belt, across Michigan Street. Historically, the neighborhood was much larger, encompassing the area where the BNMC is now located, and stretching from Main Street in the West to Best Street in the north, and Genesee Street in the east. However, the construction of the Kensington Expressway and the BNMC, as well as other developments in the surrounding area, shrank the neighborhood to its current size

An Unexpected Influence

Notes and handouts from an informal presentation at the John Carter Brown Library

Using simplicial volume to count multi-tangent trajectories of traversing vector fields

For a non-vanishing gradient-like vector field on a compact manifold $X^{n+1}$ with boundary, a discrete set of trajectories may be tangent to the boundary with reduced multiplicity $n$, which is the maximum possible. (Among them are trajectories that are tangent to $\partial X$ exactly $n$ times.) We prove a lower bound on the number of such trajectories in terms of the simplicial volume of $X$ by adapting methods of Gromov, in particular his "amenable reduction lemma". We apply these bounds to vector fields on hyperbolic manifolds.Comment: 16 pages, 5 figure