Related papers: Poincare duality in dimension 3
We extend Hendriks' classification theorem and Turaev's realisation and splitting theorems for Poincare duality complexes in dimension three to the relative case of Poincare duality pairs. The results for Poincare duality complexes are…
Using methods of KK-theory, we generalize Poincare duality to the framework of twisted K-theory.
We state a number of open questions on 3-dimensional Poincar\'e duality groups and their subgroups, motivated by considerations from 3-manifold topology.
In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.
This is the announcement of an alternative approach to the 3-dimensional Poincar\'e Conjecture, different from Perelman's big and spectacular breakthrough. No claim concerning the other parts of the Thurston Geometrization Conjecture, come…
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of Poincare duality complexes of dimension 4. Generalizing Turaev's fundamental triples of Poincare duality complexes of dimension…
This paper is an introduction to the use of the cobordism of chain complexes with Poincar\'e duality in surgery theory. It is a companion to the author's paper "An introduction to algebraic surgery" math.AT/0008071 (to appear in Volume 2 of…
In earlier work we presented necessary conditions for a fundamental triple to be that of a 3-dimensional Poincar\'e duality pair with aspherical boundary components. We provide a construction which shows that the necessary conditions are…
The purpose of this paper was to give an algebraic analog of Poincare duality. But there is a mistake in the proof of the main theorem. It will be corrected as soon as possible.
We investigate some connections between two different ways of defining Poincar\'e Duality, and relate them geometrically to the level curve mapping.
We introduce a notion of Poincar\'e duality for pairs of $\infty$-categories, extending Poincar\'e-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a…
We prove the analogue of Johannson's Deformation Theorem for PD3 pairs.
We walk out the landscape of K-theoretic Poincare Duality for finite algebras. It paves the way to get continuum Dirac operators from discrete noncommutative manifolds.
We prove duality theorems for twisted Reidemeister torsions and twisted Alexander polynomials generalizing the results of Turaev. As a corollary we determine the parity of the degrees of twisted Alexander polynomials of 3-manifolds in many…
Quark-hadron duality and its potential applications are discussed. We focus on theoretical efforts to model duality.
We present two extensions of the one dimensional free Poincar\'e inequality similar in spirit to two classical refinements.
We introduce a new class of duality symmetries amongst quantum field theories. The new class is based upon global spacetime symmetries, such as Poincare invariance and supersymmetry, in the same way as the existing duality transformations…
I summarize recent progress in the treatment of the Poincar\'e three-nucleon problem at intermediate energies
Baues and Bleille showed that, up to oriented homotopy equivalence, a Poincare duality complex of dimension $n \ge 3$ with $(n-2)$-connected universal cover, is classified by its fundamental group, orientation class and the image of its…