BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Martin Scharlemann (UC Santa Barbara)
DTSTART:20200512T153000Z
DTEND:20200512T160000Z
DTSTAMP:20260423T003243Z
UID:GaTO/6
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/6/">A s
 trong Haken's theorem</a>\nby Martin Scharlemann (UC Santa Barbara) as par
 t of Geometry and topology online\n\nLecture held in N/A.\n\nAbstract\nSup
 pose that \\(T\\) is a Heegaard splitting\nsurface for a compact orientabl
 e three-manifold \\(M\\)\; suppose\nthat \\(S\\) is a reducing sphere for 
 \\(M\\).  In 1968 Haken\nshowed that there is then also a reducing sphere 
 \\(S^*\\) for\nthe Heegaard splitting. That is\, \\(S^*\\) is a reducing s
 phere\nfor \\(M\\) and the surfaces \\(T\\) and \\(S^*\\) intersect in a\n
 single circle.  In 1987 Casson and Gordon extended the result\nto boundary
 -reducing disks in \\(M\\) and noted that in both\ncases \\(S^*\\) is obta
 ined from \\(S\\) by a sequence of\noperations called one-surgeries.  Here
  we show that in fact\none may take \\(S^* = S\\)\, at least in the case w
 here \\(M\\)\ncontains no \\(S^1 \\times S^2\\) summands.\n
LOCATION:https://researchseminars.org/talk/GaTO/6/
END:VEVENT
END:VCALENDAR