Homotopy types of subspace arrangements via diagrams of spaces

1993 ◽  
Vol 295 (1) ◽  
pp. 527-548 ◽  
Author(s):  
Günter M. Ziegler ◽  
Rade T. Živaljević
Keyword(s):  
Subspace Arrangements ◽  
Homotopy Types

Subspace Arrangements

1994 ◽  
pp. 321-370 ◽  
Author(s):  
Anders Björner
Keyword(s):  
Subspace Arrangements

scholarly journals Extreme nonuniqueness of end-sum

2020 ◽  
pp. 1-43
Author(s):  
Jack S. Calcut ◽  
Craig R. Guilbault ◽  
Patrick V. Haggerty
Keyword(s):  
Abelian Groups ◽  
Cohomology Algebra ◽  
Homotopy Types ◽  
Proper Homotopy ◽  
Open Formula

We give explicit examples of pairs of one-ended, open [Formula: see text]-manifolds whose end-sums yield uncountably many manifolds with distinct proper homotopy types. This answers strongly in the affirmative a conjecture of Siebenmann regarding nonuniqueness of end-sums. In addition to the construction of these examples, we provide a detailed discussion of the tools used to distinguish them; most importantly, the end-cohomology algebra. Key to our Main Theorem is an understanding of this algebra for an end-sum in terms of the algebras of summands together with ray-fundamental classes determined by the rays used to perform the end-sum. Differing ray-fundamental classes allow us to distinguish the various examples, but only through the subtle theory of infinitely generated abelian groups. An appendix is included which contains the necessary background from that area.

scholarly journals Strong Homotopy Types, Nerves and Collapses

2011 ◽  
Vol 47 (2) ◽  
pp. 301-328 ◽  
Author(s):  
Jonathan Ariel Barmak ◽  
Elias Gabriel Minian
Keyword(s):  
Homotopy Types
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