Connectivity of motivic H–spaces

Choudhury, Utsav

doi:10.2140/agt.2014.14.37

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Connectivity of motivic

$H\!$ –spaces

Utsav Choudhury

Algebraic & Geometric Topology 14 (2014) 37–55

DOI: 10.2140/agt.2014.14.37

Abstract

In this note we prove that the $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><mi mathvariant="double-struck">A</mi></mrow><mrow><mn>1</mn></mrow></msup></math>$ –connected component sheaf $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mrow><mi>a</mi></mrow><mrow><mo class="qopname">Nis</mo></mrow></msub><mrow><mo class="MathClass-open">(</mo><mrow><msubsup><mrow><mi>π</mi></mrow><mrow><mn>0</mn></mrow><mrow><msup><mrow><mi mathvariant="double-struck">A</mi></mrow><mrow><mn>1</mn></mrow></msup> </mrow></msubsup><mrow><mo class="MathClass-open">(</mo><mrow><mi mathvariant="bold-script">X</mi></mrow><mo class="MathClass-close">)</mo></mrow></mrow><mo class="MathClass-close">)</mo></mrow></math>$ of an $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>H</mi></math>$ –group $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="bold-script">X</mi></math>$ is $<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mrow><mi mathvariant="double-struck">A</mi></mrow><mrow><mn>1</mn></mrow></msup></math>$ –invariant.

Keywords

$\mathbb{A}^1$ –homotopy theory,

$H$ –spaces, homotopy pullback

Mathematical Subject Classification 2010

Primary: 14F42, 55P45

Secondary: 18E35

References

Publication

Received: 5 December 2012

Revised: 28 June 2013

Accepted: 1 July 2013

Preview posted: 21 November 2013

Published: 9 January 2014

Authors

Utsav Choudhury
Institut für Mathematik Universität Zürich Winterthurerstrasse 190 CH-8057 Zürich Switzerland
http://utsavchoudhury.weebly.com

Volume 14, issue 1 (2014)