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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240416T143000
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URL:https://uwaterloo.ca/pure-mathematics/events/differential-geometry-work
 ing-seminar-98
SUMMARY:Differential Geometry Working Seminar
CLASS:PUBLIC
DESCRIPTION:ALEKSANDAR MILIVOJEVIC\, DEPARTMENT OF PURE MATHEMATICS\, UNIVE
 RSITY OF\nWATERLOO\n\n\"OBSTRUCTIONS TO ALMOST COMPLEX STRUCTURES FOLLOWIN
 G MASSEY\"\n\nI will report on work in progress with Michael Albanese\, in
  which we\nprove statements claimed by Massey in 1961 concerning the obstr
 uctions\nto finding an almost complex structure on an orientable manifold 
 (or\nmore generally\, reducing the structure group of a real vector bundle
 \nover a CW complex to the unitary group). These obstructions involve\nthe
  integral Stiefel-Whitney classes – which detect the existence of\ninteg
 ral lifts of the mod 2 Stiefel-Whitney classes\, namely putative\nChern cl
 asses – and relations between the Pontryagin and Chern\nclasses. A somew
 hat surprising aspect of these obstructions is that\nthey are in fact gene
 rally proper fractional parts of what one might\nat first expect. For exam
 ple\, the obstruction in degree eleven is 1/24\nof the eleventh integral S
 tiefel-Whitney class.\n\nMC 5403
DTSTAMP:20260505T003410Z
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