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Description: |
Although the phenomenon of chirality appears in many areas of science, specially in chemistry, in mathematics it appears essentially in topological, geometrical and combinatorial forms. Chirality in maps and hypermaps (combinatorial and algebraic form of chirality) is not merely a binary invariant but can be quantified by two invariants $-$ the chirality group and the chirality index, the latter being the size of the chirality group. Every finite abelian group is the chirality group of some hypermap, whereas many non-abelian groups, including symmetric and dihedral groups, cannot arise as chirality groups. The most extreme type of chirality arises when the chirality group coincides with the monodromy group. Such hypermaps are called totally chiral. Examples of these can be constructed by considering appropriate "asymmetric" pairs of generators of certain non-abelian simple groups. In this talk we speak about chirality in maps and hypermaps giving more emphasis to the extreme form of chirality.
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