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On the Cohomology of Impossible Figures

1992/01/01 by Roger Penrose · 1 voice · 3 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #Polynomial and algebraic computation

paper · doi:10.2307/1575844

openalex publication_date 1992/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06

Abstract

the basic meaning of this concept should emerge during the course of the discussion. Here Q is some (non-simply connected) region of the plane-which I shall take to contain the 'support' (i.e. the region of the plane where the drawing occurs) of some impossible figure-and G is a (normally Abelian) group, which I shall refer to as the ambiguity group of the figure. (For those readers not familiar with the mathematical concept of a group, it may be taken that G is just some set of numbers closed under multiplication and division. Thus if a and b belong to G, then so do ab and a/b.) To fix ideas, let us consider two examples. The first is the

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