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Dihedral ∞-simplicial modules and dihedral homology of involutive homotopy unital A-algebras

  • Sergey V. Lapin EMAIL logo
Published/Copyright: April 6, 2019
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Abstract

The notion of a dihedral -simplicial module is introduced. The homotopy invariance of the structure of a dihedral -simplicial module is proved. The concept of the dihedral homology of a dihedral -simplicial module is developed. The notion of an involutive homotopy unital A-algebra is introduced. The dihedral -simplicial module is constructed using an involutive homotopy unital A-algebra. The concept of the dihedral homology of an involutive homotopy unital A-algebra is developed. For the dihedral homology of involutive homotopy unital A-algebras, the analogue of the Krasauskas–Lapin–Solov’ev exact sequence is obtained.

MSC 2010: 55U10; 18G30; 55U43

Dedicated to Professor N. Berikashvili on the occasion of his 90th birthday


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Received: 2018-10-03
Accepted: 2019-02-05
Published Online: 2019-04-06
Published in Print: 2019-06-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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