Mel Rothenberg passed away on August 1, 2023. He had been a professor at the University of Chicago since the mid 1960’s, emeritus for the past 20.
Mel was a topologist. His early work was in algebraic topology, related to the unstable version of the J-homomorphism. With Steenrod, he found a spectral sequence for the cohomology of the classifying space of an H-space.
He then moved on to geometric topology. His largest two collaborations were with Dick Lashof and with Ib Madsen. With Lashof, he made important early contributions to smoothing and triangulation theory (e.g. a proof of the triangulability of 4-connected topological manifolds), and equivariant triangulation theory. They, together with Burghelea, wrote a useful book about how surgery theory and pseudoisotopy theory combine to give a pcture of the Automorphisms of a manifold.
His work with Madsen showed that it was possible to understand odd order group actions by surgery theoretic means. Their series of seven papers included deep results about equivariant transversality and a topological signature theorem that are high points in the subject even decades later. Their work spurred on developments in the theory of stratified spaces, but even in the situation of orbifolds, the beautiful structure they discovered does not extend even to the group Z/2.
He had a love for Reidemeister torsion, and studied it for non-free actions in the smooth setting, with Lott discovered corrections to a Cheeger-Muller theorem for even dimensional smooth actions, and with Lueck and Mathai considered L^2 variants. These ideas are now of relevance in low dimensional topology and in number theory, developments he would have been glad to hear about.
He will be remembered by those who knew him for his human qualities even more than by his theorems. He was beloved by students and young faculty. His foibles (e.g. his inability to spell Lashof’s name correctly or to keep his shirt tucked in) made him accessible despite his sharpness. Mel was an inspiring, if sometimes confusing, lecturer. He would teach courses on the new theorems that he wanted to learn – making it abundantly clear that beautiful mathematics does not start out that way. You have to get messy in the lab and there’s no way to avoid thinking through all the details yourself. He taught hundreds of graduate students at Chicago, and has 111 direct mathematical descendants.
-Shmuel Weinberger
