Geometry/topology Seminar
Monday, April 10, 2017, 3:15pm, 119 Physics
Alex Pieloch (Duke University)
Moduli Spaces of Real Algebraic Curves
Abstract:- There is a natural relationship between moduli spaces of Riemann surfaces,
mapping class groups of surfaces, and intersection patterns of simple closed
curves on surfaces. In this talk, we describe an analogous relationship
between moduli spaces of real algebraic curves, mapping class groups of
surfaces with orientation reversing involutions, and intersection patterns
of involution invariant simple closed curves on surfaces. After
establishing these relationships, we obtain that the homology and cohomology
groups of mapping class groups of surfaces with orientation reversing
involutions satisfy duality relationships analogous to those for compact
manifolds. We also obtain that higher homotopy groups associated to the
moduli spaces of real algebraic curves relative to its boundary vanish in
all degrees less than a determinable constant. [video]
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