Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

Institut for Matematiske Fag

Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

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Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group. / Foley, John D.

I: Mathematische Zeitschrift, Bind 301, Nr. 3, 2022, s. 2465-2496.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Foley, JD 2022, 'Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group', Mathematische Zeitschrift, bind 301, nr. 3, s. 2465-2496. https://doi.org/10.1007/s00209-022-02981-1

APA

Foley, J. D. (2022). Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group. Mathematische Zeitschrift, 301(3), 2465-2496. https://doi.org/10.1007/s00209-022-02981-1

Vancouver

Foley JD. Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group. Mathematische Zeitschrift. 2022;301(3):2465-2496. https://doi.org/10.1007/s00209-022-02981-1

Author

Foley, John D. / Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group. I: Mathematische Zeitschrift. 2022 ; Bind 301, Nr. 3. s. 2465-2496.

Bibtex

@article{7731f5bd77c64004a08780cb903e8d88,

title = "Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group",

abstract = "This paper extends certain characterizations of nullhomotopic maps between p-compact groups to maps with target the p-completed classifying space of a connected Kac–Moody group and source the classifying space of either a p-compact group or a connected Kac–Moody group. A well known inductive principle for p-compact groups is applied to obtain general, mapping space level results. An arithmetic fiber square computation shows that a null map from the classifying space of a connected compact Lie group to the classifying space of a connected topological Kac–Moody group can be detected by restricting to the maximal torus. Null maps between the classifying spaces of connected topological Kac–Moody groups cannot, in general, be detected by restricting to the maximal torus due to the nonvanishing of an explicit abelian group of obstructions described here. Nevertheless, partial results are obtained via the application of algebraic discrete Morse theory to higher derived limit calculations. These partial results show that null maps are detected by restricting to the maximal torus in many cases of interest.",

keywords = "Algebraic discrete Morse theory, Arithmetic fiber square, Homotopical group theory, Invariant theory, Kac–Moody groups, p-Compact groups",

author = "Foley, {John D.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

doi = "10.1007/s00209-022-02981-1",

language = "English",

volume = "301",

pages = "2465--2496",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer",

number = "3",

}

RIS

TY - JOUR

T1 - Recognizing nullhomotopic maps into the classifying space of a Kac–Moody group

AU - Foley, John D.

PY - 2022

Y1 - 2022

N2 - This paper extends certain characterizations of nullhomotopic maps between p-compact groups to maps with target the p-completed classifying space of a connected Kac–Moody group and source the classifying space of either a p-compact group or a connected Kac–Moody group. A well known inductive principle for p-compact groups is applied to obtain general, mapping space level results. An arithmetic fiber square computation shows that a null map from the classifying space of a connected compact Lie group to the classifying space of a connected topological Kac–Moody group can be detected by restricting to the maximal torus. Null maps between the classifying spaces of connected topological Kac–Moody groups cannot, in general, be detected by restricting to the maximal torus due to the nonvanishing of an explicit abelian group of obstructions described here. Nevertheless, partial results are obtained via the application of algebraic discrete Morse theory to higher derived limit calculations. These partial results show that null maps are detected by restricting to the maximal torus in many cases of interest.

AB - This paper extends certain characterizations of nullhomotopic maps between p-compact groups to maps with target the p-completed classifying space of a connected Kac–Moody group and source the classifying space of either a p-compact group or a connected Kac–Moody group. A well known inductive principle for p-compact groups is applied to obtain general, mapping space level results. An arithmetic fiber square computation shows that a null map from the classifying space of a connected compact Lie group to the classifying space of a connected topological Kac–Moody group can be detected by restricting to the maximal torus. Null maps between the classifying spaces of connected topological Kac–Moody groups cannot, in general, be detected by restricting to the maximal torus due to the nonvanishing of an explicit abelian group of obstructions described here. Nevertheless, partial results are obtained via the application of algebraic discrete Morse theory to higher derived limit calculations. These partial results show that null maps are detected by restricting to the maximal torus in many cases of interest.

KW - Algebraic discrete Morse theory

KW - Arithmetic fiber square

KW - Homotopical group theory

KW - Invariant theory

KW - Kac–Moody groups

KW - p-Compact groups

UR - http://www.scopus.com/inward/record.url?scp=85125035599&partnerID=8YFLogxK

U2 - 10.1007/s00209-022-02981-1

DO - 10.1007/s00209-022-02981-1

M3 - Journal article

AN - SCOPUS:85125035599

VL - 301

SP - 2465

EP - 2496

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 3

ER -

ID: 310972629