EVENT DETAILS AND ABSTRACT

Title: Revisiting the Stable Adams conjecture
Speaker: Prasit Bhattacharya
Speaker Info: University of Virginia
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Special Note:
Abstract:

The Adams conjecture, perhaps one of the most celebrated result in the subject of stable homotopy theory, was resolved Quillen and Sullivan independently in 1970s. Essentially, the Adams conjecture claims that that the Adams operation $\psi^q:BU \to BU$ composed with the $J$-homomorphism $J: BU \to BGL_1(S)$ homomorphism is homotopic to the $J$, after localizing away from $q$. Here $GL_1(S)$ denote the units of the sphere spectrum. The stable version of Adams conjecture states that $J$ can be deformed to $J \circ \psi^q$ via the space of infinite loop space maps from $BU_{1/q} \to BGL_1(S)_{1/q}$. The stable version of Adams conjecture was resolved by Friedlander (1980) and remains the only accepted proof. However, we suspect there might be a lacuna in Friedlander’s proof. In this talk, I will revisit this ofFriedlander and explain a possible fix. This work is joint with N. Kitchloo.