M -equivalences and homotopy colimits

David Blanc; Robert D. Thompson

doi:10.1090/conm/181

M -equivalences and homotopy colimits

David Blanc, Robert D. Thompson

Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Given a fixed "model space" M, we call a map f: X-+ Y an M-equivalence if it induces a weak equivalence f.: xM-+ yM on mapping spaces. We discuss the following question: under what conditions do homotopy colimits preserve M-equivalences? For certain M's of interest,
this is shown to depend precisely on the connectivities of the spaces.

Original language	English
Title of host publication	The Čech Centennial
Subtitle of host publication	A Conference on Homotopy Theory
Editors	Jonathan Rosenberg, Stephan Stolz
Publisher	American Mathematical Society
Pages	27–33
Number of pages	7
ISBN (Electronic)	978-0-8218-7772-2
ISBN (Print)	978-0-8218-0296-0, 0-8218-0296-8
DOIs	https://doi.org/10.1090/conm/181
State	Published - 1995

Publication series

Name	Contemporary Mathematics
Publisher	American Mathematical Society
Number	181

Keywords

Combinatorics
Cyclic group
Fundamental group
Group (mathematics)
Manifold
Mathematics
Order (group theory)
Scalar curvature
Simply connected space
Trivial group

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10.1090/conm/181

Cite this

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AU - Thompson, Robert D.

PY - 1995

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AB - Given a fixed "model space" M, we call a map f: X-+ Y an M-equivalence if it induces a weak equivalence f.: xM-+ yM on mapping spaces. We discuss the following question: under what conditions do homotopy colimits preserve M-equivalences? For certain M's of interest,this is shown to depend precisely on the connectivities of the spaces.

KW - Combinatorics

KW - Cyclic group

KW - Fundamental group

KW - Group (mathematics)

KW - Manifold

KW - Mathematics

KW - Order (group theory)

KW - Scalar curvature

KW - Simply connected space

KW - Trivial group

UR - https://math.haifa.ac.il/blanc/Blanc_Thompson-M-equivs.pdf

U2 - 10.1090/conm/181

DO - 10.1090/conm/181

M3 - Conference contribution

SN - 978-0-8218-0296-0

SN - 0-8218-0296-8

T3 - Contemporary Mathematics

SP - 27

EP - 33

BT - The Čech Centennial

A2 - Rosenberg, Jonathan

A2 - Stolz, Stephan

PB - American Mathematical Society

ER -

M -equivalences and homotopy colimits

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