BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Infinite loop spaces and positive scalar curvature
- Oscar Randal-Williams\, Cambridge
DTSTART;TZID=Europe/London:20131016T160000
DTEND;TZID=Europe/London:20131016T170000
UID:TALK46417AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/46417
DESCRIPTION:It is well known that there are topological obstru
ctions to a manifold $M$ admitting a Riemannian me
tric of everywhere positive scalar curvature (psc)
: if $M$ is Spin and admits a psc metric\, the Lic
hnerowiczâ€“WeitzenbĂ¶ck formula implies that the Dir
ac operator of $M$ is invertible\, so the vanishin
g of the $\\hat{A}$ genus is a necessary topologic
al condition for such a manifold to admit a psc me
tric. If $M$ is simply-connected as well as Spin\,
then deep work of Gromov--Lawson\, Schoen--Yau\,
and Stolz implies that the vanishing of (a small r
efinement of) the $\\hat{A}$ genus is a sufficient
condition for admitting a psc metric. For non-sim
ply-connected manifolds\, sufficient conditions fo
r a manifold to admit a psc metric are not yet und
erstood\, and are a topic of much current research
.\n\nI will discuss a related but somewhat differe
nt problem: if $M$ does admit a psc metric\, what
is the topology of the space $\\mathcal{R}(M)$ of
all psc metrics on it? Recent work of V. Chernysh
and M. Walsh shows that this problem is unchanged
when modifying $M$ by certain surgeries\, and I wi
ll explain how this can be used along with work of
Galatius and the speaker to show that the algebra
ic topology of $\\mathcal{R}(M)$ for $M$ of dimen
sion at least 6 is "as complicated as can possibly
be detected by index-theory". This is joint work
with Boris Botvinnik and Johannes Ebert.\n
LOCATION:MR13
CONTACT:Ivan Smith
END:VEVENT
END:VCALENDAR