BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeff Carlson (Imperial College London) DTSTART:20211117T204500Z DTEND:20211117T220000Z DTSTAMP:20260404T150744Z UID:rts/3 DESCRIPTION:Title: Products on Tor\, homogeneous spaces\, and Borel cohomology\nby Jef f Carlson (Imperial College London) as part of Rochester topology seminar\ n\nLecture held in Hylan 1106A.\n\nAbstract\nThe Eilenberg-Moore spectral sequence converges from the classical Tor of a span of cohomology rings to the differential Tor of a span of cochain algebras (which is the cohomolo gy of the homotopy pullback). These are both rings\, the first classically and the second as a corollary of the Eilenberg-Zilber theorem. \n\nOne mi ght well ask when a more general differential Tor of DGAs admits a ring st ructure\, though apparently no one did. We will show that when the DGAs in question admit a certain sort of $E_3$-algebra structure\, Tor is a commu tative graded algebra. \n\nWe have not done this out of an innocent intere st in homotopy-commutative algebras. In 1960s and '70s there was a flurry of activity developing A-infinity-algebraic techniques with an aim toward computing the Eilenberg–Moore spectral sequence (for example\, of a loop space or homogeneous space). Arguably the most powerful result this progr am produced was the 1974 theorem of Munkholm that the sequence collapses w hen the three input spaces have polynomial cohomology over a given princip al ideal domain\, which however only gives the story on cohomology groups. Our result shows that Munkholm's map is in fact an isomorphism of rings. \n\nThe proof hinges on homotopy properties of the (1-)category of augment ed DGAs. This work is all joint with several large commutative diagrams\, who should be considered the true authors.\n\nZoom meeting ID: 988 2359 98 95 passcode: 553391\n LOCATION:https://stable.researchseminars.org/talk/rts/3/ END:VEVENT END:VCALENDAR