New Proofs of Chapman's Ce Mapping Theorem and West's Mapping Cylinder Theorem

1977 ◽  
Vol 67 (2) ◽  
pp. 327 ◽  
Author(s):  
A. Fathi ◽  
A. Marin ◽  
Y. M. Visetti
Keyword(s):  
Mapping Cylinder ◽  
Cylinder Theorem

scholarly journals New proofs of Chapman’s ${\rm CE}$ mapping theorem and West’s mapping cylinder theorem

1977 ◽  
Vol 67 (2) ◽  
pp. 327-327
Author(s):  
A. Fathi ◽  
A. Marin ◽  
Y. M. Visetti
Keyword(s):  
Mapping Cylinder ◽  
Cylinder Theorem

Three-cylinder theorem for a certain class of semilinear parabolic equations

1992 ◽  
Vol 51 (1) ◽  
pp. 21-27 ◽  
Author(s):  
A. A. Varin
Keyword(s):  
Parabolic Equations ◽  
Semilinear Parabolic Equations ◽  
Cylinder Theorem ◽  
Semilinear Parabolic

A proof of the comparison theorem for spectral sequences

1957 ◽  
Vol 53 (1) ◽  
pp. 57-62 ◽  
Author(s):  
E. C. Zeeman
Keyword(s):  
Comparison Theorem ◽  
Analogous Result ◽  
Spectral Sequences ◽  
Mapping Cylinder ◽  
Fibre Space ◽  
The Third

The comparison theorem is an algebraic theorem, which corresponds to the following topological situation. A map between two fibre spaces induces a homomorphism between the two corresponding spectral sequences relating the homologies of the base, fibre and fibre space; if the map induces an isomorphism on any two of these quantities, then it also does on the third. J. C. Moore (l) proved the theorem using a mapping cylinder, which requires that the spectral sequences arise from filtered differential groups. The present proof assumes only the existence of the spectral sequences from the E2 terms onwards. Moreover, we generalize the theorem, assuming that the homomorphisms on the two given quantities are isomorphic only up to given dimensions, and deducing the same for the third quantity. For algebraic translucence we use a simpler hypothesis (property (iii)) than Moore's concerning the E2 terms. However, if his hypothesis is assumed, together with the existence of E1 terms, then his theorem can be deduced as a corollary. The analogous result for cohomology is similar, and is stated at the end.

scholarly journals A complex analogue of Hartman-Nirenberg cylinder theorem

1972 ◽  
Vol 7 (3-4) ◽  
pp. 453-460 ◽  
Author(s):  
Kinetsu Abe
Keyword(s):  
Complex Analogue ◽  
Cylinder Theorem

scholarly journals Dupin hypersurfaces, group actions and the double mapping cylinder

1987 ◽  
Vol 26 (3) ◽  
pp. 429-459 ◽  
Author(s):  
Karsten Grove ◽  
Stephen Halperin
Keyword(s):  
Group Actions ◽  
Mapping Cylinder ◽  
Dupin Hypersurfaces

The cylinder theorem in $${{\mathcal {H}}}^2\times R$$

2020 ◽  
Vol 111 (3) ◽  
Author(s):  
João Lucas Marques Barbosa ◽  
Manfredo Perdigão do Carmo
Keyword(s):  
Cylinder Theorem

scholarly journals An affine analogue of the Hartman-Nirenberg cylinder theorem

2002 ◽  
Vol 322 (3) ◽  
pp. 573-582
Author(s):  
Maks A. Akivis ◽  
Vladislav V. Goldberg
Keyword(s):  
Cylinder Theorem

On simple maps

2013 ◽  
Author(s):  
Friedhelm Waldhausen ◽  
Bjørn Jahren ◽  
John Rognes
Keyword(s):  
Homotopy Type ◽  
Geometric Realization ◽  
Homotopy Equivalence ◽  
Mapping Cylinder ◽  
Simplicial Sets ◽  
Weak Homotopy ◽  
Formal Properties ◽  
Weak Homotopy Equivalence

This chapter deals with simple maps of finite simplicial sets, along with some of their formal properties. It begins with a discussion of simple maps of simplicial sets, presenting a proposition for the conditions that qualify a map of finite simplicial sets as a simple map. In particular, it considers a simple map as a weak homotopy equivalence. Weak homotopy equivalences have the 2-out-of-3 property, which combines the composition, right cancellation and left cancellation properties. The chapter proceeds by defining some relevant terms, such as Euclidean neighborhood retract, absolute neighborhood retract, Čech homotopy type, and degeneracy operator. It also describes normal subdivision of simplicial sets, geometric realization and subdivision, the reduced mapping cylinder, how to make simplicial sets non-singular, and the approximate lifting property.

scholarly journals Proof of semialgebraic covering mapping cylinder conjecture with semialgebraic covering homotopy theorem

2007 ◽  
Vol 154 (1) ◽  
pp. 69-89 ◽  
Author(s):  
Myung-Jun Choi ◽  
Dae Heui Park ◽  
Dong Youp Suh
Keyword(s):  
Mapping Cylinder ◽  
Covering Mapping

scholarly journals Mapping Cylinder Neighborhoods of Some ANR's

1976 ◽  
Vol 103 (3) ◽  
pp. 417 ◽  
Author(s):  
R. T. Miller
Keyword(s):  
Mapping Cylinder
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