For a given pair of maps f, g : X → M from an arbitrary topological space to an n-manifold, the Lefschetz homomorphism is a certain graded homomorphism Λfg : H(X) → H(M) of degree (−n). We prove a Lefschetztype coincidence theorem: if the Lefschetz homomorphism is nontrivial then there is an x ∈ X such that f(x) = g(x).

We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems, surjective homomorphism problems seem to be harder to classify and we examine especially three concrete problems that have arisen from the literature, two of which r...

A knot in a solid torus defines map on the set of (smooth or topological) concordance classes knots S 3 S^3 ...

This paper describes an augmented reality system that incorporates a real-time dense stereo vision system. Analysis of range and intensity data is used to perform two functions: 1) 3D detection and tracking of the user’s fingertip or a pen to provide natural 3D pointing gestures, and 2) computation of the 3D position and orientation of the user’s viewpoint without the need for fiducial marks ca...

We consider the effect of interference on the convergence rate of a class of distributed averaging algorithms called consensus algorithms, which iteratively compute the measurement average by message passing among nodes. It is usually assumed that these algorithms converge faster with a greater exchange of information (i.e., by increased network connectivity) in every iteration. However, when t...