Just as a symmetric surface with separating fixed locus halves into two oriented bordered surfaces, an arbitrary symmetric surface halves into two oriented symmetric half-surfaces, i.e. surfaces with crosscaps. Motivated in part by the string theory view of real Gromov-Witten invariants, we previously introduced moduli spaces of maps from surfaces with crosscaps, developed the relevant Fredholm...

We prove that a (2m n+1)-connectedmap f : Mm ! Xn from a compact PL m-manifoldM to a generalized n-manifoldX with the disjoint disks property, 3m 2n 2, is homotopic to a tame embedding. There is also a controlled version of this result, as well as a version for noncompactM and proper maps f that are properly (2m n+ 1)-connected. The techniques developed lead to a general position result for arb...

Genetic maps are used routinely in family-based linkage studies to identify the rough location of genes that influence human traits and diseases. Unlike physical maps, genetic maps are based on the amount of recombination occurring between adjacent loci rather than the actual number of bases separating them. Genetic maps are constructed by statistically characterizing the number of crossovers o...

In this paper we present a new concept of robot-dependent reachability map (RDReachMap) for mobile platforms. In heterogeneous multi-robot systems, the reachability limit of robots motion and actuation must be considered when assigning tasks to them. We created an algorithm that generates those reachability maps, separating regions that can be covered by a robot from the unreachable ones, using...