# Topology Seminar

tmf Is Not a Ring Spectrum Quotient

Carl McTague, Rochester

3:40 PM - 4:40 PM

Hylan 1106A

To begin, I will describe a new result on the greatest common divisor of binomial coefficients A result related to the geometry of manifolds, answering a question raised the last time I spoke in this seminar, and recently published in the Amer. Math. Monthly.

Next, I will describe a new proof that is not a ring spectrum quotient of . In fact, for any prime and any sequence of homogeneous elements of , the -module

is not (even abstractly) isomorphic to . The key is showing that, for any commutative ring spectrum and any sequence of homogeneous elements of , there is an isomorphism of graded -vector spaces

where the right-hand side is the rational homology of the (total) Koszul complex of , which is strictly bigger than unless is a -quasi-regular sequence. The result then follows from the fact that the kernel of the -local Witten genus cannot be generated by a -quasi-regular sequence.

Event contact: carl dot mctague at rochester dot edu

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