The wild world of 4-manifolds
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Physics - Math Colloquium

Prof. Dr. Cihan Saçlıoğlu, Sabancı University, İstanbul

Title: The wild world of 4-manifolds

Date/Time: Aprl. 25 Wednesday at 10:40

Place: SUNUM Building G-111

Tea, coffee and cookies @ 10:15 in SUNUM Hall.


Four-manifolds first came into physics through Einstein's General theory of
relativity, which relates large-scale gravitational phenomena to the
metric-based Riemannian curvature of space-time.  In the mathematical study
of manifolds, on the other hand, a fundamental problem is the classification
of manifolds in all dimensions through their topological and other invariants.
In 1956, Milnor exhibited 28 spheres in 7 dimensions which were topologically
indistinguishable, but differentiably inequivalent.  This surprising
proliferation of so-called "exotic" or "fake" versions of the same topological
manifold starts at dimension 4, which is also where the most bizarre varieties
are found.  For example, there are uncountably many "fake" R^4's, a phenomenon
not encountered in any other dimension.  We'll give an overview of the field
and offer a speculation about its possible relevance to physics.

Contact: İnanç Adagideli,

  and/or Cem Çelebi,