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Homotopy 4-spheres and generalized square knots

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Alex Zupan
University of Nebraska Lincoln
Thu, 2019-09-19 16:30 - 17:20
MPIM Lecture Hall

The Smooth 4-dimensional Poincaré Conjecture (S4PC) asserts that every homotopy 4-sphere is diffeomorphic to the standard 4-sphere $S^4$.  We prove a special case of the S4PC:  If $X$ is a homotopy 4-sphere that can be built with two 2-handles and two 3-handles, and such that one component of the 2-handle attaching link $L$ is a generalized square knot $T(p,q) \# T(-p,q)$, then $X$ is diffeomorphic to $S^4$.  This is joint work with Jeffrey Meier.

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