Baues, Hans Joachim; Bleile, Beatrice

Author(s)

Baues, Hans Joachim

Bleile, Beatrice

Publication Date

2008

Abstract

We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD⁴-complexes. Generalizing Turaev's fundamental triples of PD³-complexes we introduce fundamental triples of PDⁿ-complexes and show that two PDⁿ complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional manifolds.

Citation

Algebraic & Geometric Topology, v.8, p. 2355-2389

ISSN

1472-2739

1472-2747

Link

https://hdl.handle.net/1959.11/3032

Publisher

Mathematical Sciences Publishers

Title

Poincaré duality complexes in dimension four

Type of document

Journal Article

Entity Type

Publication

Author(s)	Baues, Hans Joachim Bleile, Beatrice
Publication Date	2008
Abstract	We describe an algebraic structure on chain complexes yielding algebraic models which classify homotopy types of PD⁴-complexes. Generalizing Turaev's fundamental triples of PD³-complexes we introduce fundamental triples of PDⁿ-complexes and show that two PDⁿ complexes are orientedly homotopy equivalent if and only if their fundamental triples are isomorphic. As applications we establish a conjecture of Turaev and obtain a criterion for the existence of degree 1 maps between n-dimensional manifolds.
Citation	Algebraic & Geometric Topology, v.8, p. 2355-2389
ISSN	1472-2739 1472-2747
Link	https://hdl.handle.net/1959.11/3032
Publisher	Mathematical Sciences Publishers
Title	Poincaré duality complexes in dimension four
Type of document	Journal Article
Entity Type	Publication

Poincaré duality complexes in dimension four

Files: