TY - JOUR
T1 - Classifying spaces for 1-truncated compact lie groups
AU - Rezk, Charles
N1 - Funding Information:
Acknowledgments I thank Peter May for comments on a draft of this paper. The author was supported under NSF grant DMS-1406121.
Publisher Copyright:
© 2018, Mathematical Sciences Publishers. All rights reserved.
PY - 2018/1/10
Y1 - 2018/1/10
N2 - A 1-truncated compact Lie group is any extension of a finite group by a torus. In this note we compute the homotopy types of Map * (BG,BH), Map(BG,BH), and Map(EG,BGH) for compact Lie groups G and H with H 1-truncated, showing that they are computed entirely in terms of spaces of homomorphisms from G to H. These results generalize the well-known case when H is finite, and the case when H is compact abelian due to Lashof, May, and Segal.
AB - A 1-truncated compact Lie group is any extension of a finite group by a torus. In this note we compute the homotopy types of Map * (BG,BH), Map(BG,BH), and Map(EG,BGH) for compact Lie groups G and H with H 1-truncated, showing that they are computed entirely in terms of spaces of homomorphisms from G to H. These results generalize the well-known case when H is finite, and the case when H is compact abelian due to Lashof, May, and Segal.
KW - Classifying spaces
KW - Equivariant
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U2 - 10.2140/agt.2018.18.525
DO - 10.2140/agt.2018.18.525
M3 - Article
AN - SCOPUS:85040934558
SN - 1472-2747
VL - 18
SP - 525
EP - 546
JO - Algebraic and Geometric Topology
JF - Algebraic and Geometric Topology
IS - 1
ER -