## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Local algebraic structures and topological manifolds

**Speaker:** Nathaniel Rounds

**Speaker Info:** Purdue

**Brief Description:**

**Special Note**:

**Abstract:**

Can we associate an algebraic structure to a manifold such
that this structure up to equivalence determines the manifold up to
homeomorphism? If we replace the word "homeomorphism" with the word
"homotopy equivalence", the answer is yes. We will describe various
algebraic structures on a manifold's chains and cochains, all of which
are known to be homotopy invariant. We will suggest, however, that
the missing idea is that of algebraic locality. The various algebraic
structures that we associate to a manifold are all local in an
appropriate sense, but the inverse to the Poincare duality map need
not be local. We will show, using Ranicki's algebraic surgery, that
considering the inverse to the Poincare duality map leads to a
topological invariant of manifolds. We will end with a conjectural
synthesis of all these ideas which gives an affirmative answer to the
opening question.

**Date:** Monday, April 4, 2011

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Prof. Paul Goerss

**Contact email:** pgoerss@math.northwestern.edu

**Contact Phone:** 847-491-8544

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