tmf Is Not a Ring Spectrum Quotient of String Bordism

This paper shows that $\mathrm{tmf}[1/6]$ is not a ring spectrum quotient of $\mathrm{MO}\langle8\rangle[1/6]$. In fact, for any prime $p>3$ and any sequence $X$ of homogeneous elements of $\pi_*\mathrm{MO}\langle8\rangle$, the $\pi_*\mathrm{MO}\langle8\rangle$-module $$\pi_*\big(\mathrm{MO}\langle8\rangle_{(p)}/X\big)$$ is not (even abstractly) isomorphic to $\pi_*\mathrm{tmf}_{(p)}$. It does so by showing that, for any commutative ring spectrum $R$ and any sequence $X$ of homogeneous elements of $\pi_*(R)$, there is an isomorphism of graded $\mathbf{Q}$-vector spaces $$\pi_*(R/X)\otimes\mathbf{Q} \cong \mathrm{H}_*(\mathrm{Tot}(\mathrm{K}(X)))\otimes\mathbf{Q},$$ where the right-hand side is the rational homology of the (total) Koszul complex of $X$, which is strictly bigger than $\pi_*(R)/(X)\otimes\mathbf{Q}$ unless $X$ is a $\pi_*(R)\otimes\mathbf{Q}$-quasi-regular sequence. The result then follows from the fact that the kernel of the $p$-local Witten genus cannot be generated by a $\pi_*\mathrm{MO}\langle8\rangle\otimes\mathbf{Q}$-quasi-regular sequence.Comment: 9 pages; statement of the new Theorem 3 made cleare

Only a Cigarette

I lift my cigarette. In habitual man-gesture, He pats his pockets, Then takes the matches from the table. Our eyes meet As he strikes awareness To illumination..

Revisiting Hapworth : The Catharsis of Buddy Glass

J.D. Salinger\u27s Hapworth 16, 1924, his last published work, is notorious for the initial critical silence it received, as well as the subsequent general consensus that it was a text to revile if not avoid. This thesis proposes that while Hapworth is a difficult and perplexing piece, there is a good deal about it that deserves if not outright praise, then a close critical re-examination. Assuming the author of the story is not the seven-year-old version of A Perfect Day for Bananafish suicide Seymour Glass, as the story purports, but his grieving younger brother Buddy, who has spent the years since his brother\u27s death trying to come to terms with it. Hapworth is Buddy\u27s final--and perhaps finally successful--attempt to do so