Topology Seminar- Even complexes have a spherical basis

Speaker: Paul Kainen (Georgetown University)
Date and time: Thursday, November 1, 5:15--6:30pm
Place: Gelman Library, room 608
Title:Even complexes have a spherical basis

Abstract: An n-complex is even if each n-1-cell is a face of a positive even number of n-cells.  It is shown that there exists a basis (w.r.t. symmetric difference) consisting of minimum topologicalsphere-subcomplexes (of the cube or simplex) such that each even subcomplex is the sum of a unique subset of the basis, and the cardinality of the basis is determined in two different ways. Algebraic topology is used in one of the arguments.

BioPaul Kainen got his Ph.D. in Algebraic Topology under direction of Peter J. Hilton (at Cornell in prehistoric days).  He works in graph theory and its enrichments to neural networks and also category theory.  He has taught at Georgetown Univ. since 1997 and previously has worked for Bell Laboratories and for a local systems engineering company.  Kainen is especially interested in the quantitative analysis of photonic technology in medicine. His Erdos-number is 1; he is co-author of The Four-Color Problem book.