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Making connections to the big ideas in mathematics: Promoting proportional reasoning
big ideas mathematics
2015/5/29
The focus of this paper is on
proportional reasoning, emphasising
its pervasiveness throughout the
mathematics curriculum, but also
highlighting its elusiveness.
In [4] we defined a notion of parallel transport along superpaths in a supermanifold coming from a vector bundle with connection over the supermanifold. In this note, we show that the converse is also...
A Kohno-Drinfeld theorem for the monodromy of cyclotomic KZ connections
Kohno-Drinfeld theorem cyclotomic KZ connections
2010/11/23
We compute explicitly the monodromy representations of "cyclotomic" analogs of the Knizhnik--Zamolodchikov differential system. These are representations of the type B braid group $B_n^1$. We show ho...
Different versions for defining Ashtekar's generalized connections are investigated depending on the chosen smoothness category for the paths and graphs -- the label set for the projective limit. Our ...
New moduli spaces of pointed curves and pencils of flat connections
New moduli spaces pointed curves pencils flat connections
2010/10/29
It is well known that formal solutions to the Associativity Equations are the same as cyclic algebras over the homology operad $(H_*(\bar{M}_{0,n+1}))$ of the moduli spaces of $n$--pointed stable cur...