scholarly journals Obstruction theory in model categories

2004 ◽  
Vol 181 (2) ◽  
pp. 396-416 ◽  
Author(s):  
J.Daniel Christensen ◽  
William G. Dwyer ◽  
Daniel C. Isaksen
Keyword(s):  
Obstruction Theory ◽  
Model Categories

scholarly journals Comparing homotopy categories

2007 ◽  
Vol 2 (1) ◽  
pp. 169-205 ◽  
Author(s):  
David Blanc
Keyword(s):  
Exact Sequence ◽  
Obstruction Theory ◽  
Homotopy Groups ◽  
Model Categories

AbstractGiven a suitable functor T : → between model categories, we define a long exact sequence relating the homotopy groups of any X ε with those of TX, and use this to describe an obstruction theory for lifting an object G ε to . Examples include finding spaces with given homology or homotopy groups.

scholarly journals On the construction of functorial factorizations for model categories

2013 ◽  
Vol 13 (2) ◽  
pp. 1089-1124 ◽  
Author(s):  
Tobias Barthel ◽  
Emily Riehl
Keyword(s):  
Model Categories

scholarly journals The integral cohomology of the Hilbert scheme of points on a surface

2020 ◽  
Vol 8 ◽  
Author(s):  
Burt Totaro
Keyword(s):  
Natural Number ◽  
Hilbert Scheme ◽  
Obstruction Theory ◽  
Projective Surface ◽  
Hilbert Schemes ◽  
Complex Projective Surface ◽  
Smooth Complex ◽  
Hilbert Scheme Of Points ◽  
Complex Projective ◽  
Torsion Free

Abstract We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme $X^{[n]}$ has torsion-free cohomology for every natural number n. This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas’s reduced obstruction theory for nested Hilbert schemes of surfaces.

Model Categories

2009 ◽  
pp. 65-138
Author(s):  
Paul G. Goerss ◽  
John F. Jardine
Keyword(s):  
Model Categories

scholarly journals Obstruction theory on 8-manifolds

2008 ◽  
Vol 127 (2) ◽  
pp. 167-186 ◽  
Author(s):  
Martin Čadek ◽  
Michael Crabb ◽  
Jiří Vanžura
Keyword(s):  
Obstruction Theory
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