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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260922T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-viktor-majewski-non
SUMMARY:Differential Geometry Working Seminar | Viktor Majewski |\nNon-Exis
 tence of Smooth Full-Holonomy Cayley Fibrations
CLASS:PUBLIC
DESCRIPTION:VIKTOR MAJEWSKI (UNIVERSITY OF WATERLOO) \n_Non-Existence of Sm
 ooth Full-Holonomy Cayley Fibrations_ \nIn this talk\, I complete the proo
 f that every Cayley fibration of a\ncompact torsion-free Spin(7)-manifold 
 with full holonomy must have\nsingular fibers. This confirms a long-standi
 ng expectation in the\nstudy of calibrated fibrations with exceptional hol
 onomy. Last\nsemester\, I showed that using the rigidity of the Spin(7)-st
 ructure to\nreduce any hypothetical nonsingular Cayley fibration to two po
 ssible\ntopological configurations. This time\, I exclude both by proving 
 a new\nspinnability theorem for smooth fiber bundles over simply-connected
 \n4-manifolds with fiber homeomorphic to the elliptic surfaces E(2) or\nE(
 4). The E(4) case\, which constitutes the main new difficulty\, is\nestabl
 ished by combining families Seiberg–Witten theory with\nparametrized equ
 ivariant homotopy theory and equivariant K-theory. \nMC 5417
DTSTAMP:20260917T145208Z
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