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Algebraic Geometry Commons

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Full-Text Articles in Algebraic Geometry

The Galois Correspondence For Branched Covering Spaces And Its Relationship To Hecke Algebras, Matthew Ong Nov 2002

The Galois Correspondence For Branched Covering Spaces And Its Relationship To Hecke Algebras, Matthew Ong

Mathematical Sciences Technical Reports (MSTR)

There is a very beautiful correspondence between branched covers of the Riemann sphere P1 and subgroups of the fundamental group π1(P1 − {branch points}), exactly analogous to the correspondence between subfields of an algebraic extension E/F and subgroups of the Galois group Gal(E/F). This paper explores the concept of a Hecke algebra, which in this context is a generalization of the Galois group to the case of non- Galois covers S/P1. Specifically, we show that the isomorphism type of a Hecke algebra C[H\G/H] is completely determined by the decomposition of …


Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan Jan 2002

Intrinsic Knotting And Linking Of Complete Graphs, Erica Flapan

Pomona Faculty Publications and Research

We show that for every m∈N, there exists an n∈N such that every embedding of the complete graph Kn in R3 contains a link of two components whose linking number is at least m. Furthermore, there exists an r∈N such that every embedding of Kr in R3 contains a knot Q with |a2(Q)| ≥ m, where a2(Q) denotes the second coefficient of the Conway polynomial of Q.


Like A Bridge Over Colored Water: A Mathematical Review Of The Rainbow Bridge: Rainbows In Art, Myth, And Science, John A. Adam Jan 2002

Like A Bridge Over Colored Water: A Mathematical Review Of The Rainbow Bridge: Rainbows In Art, Myth, And Science, John A. Adam

Mathematics & Statistics Faculty Publications

Commenting on a recent book, the author discusses various views of the rainbow: its role in culture, its scientific description, and its mathematical theory.