- Provides new tools to address the problem of extending the Quillen approach to a more general category of spaces
- Opens a field of vision to solve old problems and pose new questions
- Winner of the 2020 Ferran Sunyer i Balaguer Prize
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- About this book
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Since the birth of rational homotopy theory, the possibility of extending the Quillen approach – in terms of Lie algebras – to a more general category of spaces, including the non-simply connected case, has been a challenge for the algebraic topologist community. Despite the clear Eckmann-Hilton duality between Quillen and Sullivan treatments, the simplicity in the realization of algebraic structures in the latter contrasts with the complexity required by the Lie algebra version.
In this book, the authors develop new tools to address these problems. Working with complete Lie algebras, they construct, in a combinatorial way, a cosimplicial Lie model for the standard simplices. This is a key object, which allows the definition of a new model and realization functors that turn out to be homotopically equivalent to the classical Quillen functors in the simply connected case. With this, the authors open new avenues for solving old problems and posing new questions.
This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.
- Table of contents (12 chapters)
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Background
Pages 17-52
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The Quillen Functors L, C and their Duals A , E
Pages 53-69
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Complete Differential Graded Lie Algebras
Pages 71-91
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Maurer–Cartan Elements and the Deligne Groupoid
Pages 93-115
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The Lawrence–Sullivan Interval
Pages 117-130
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Table of contents (12 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Lie Models in Topology
- Authors
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- Urtzi Buijs
- Yves Félix
- Aniceto Murillo
- Daniel Tanré
- Series Title
- Progress in Mathematics
- Series Volume
- 335
- Copyright
- 2020
- Publisher
- Birkhäuser Basel
- Copyright Holder
- Springer Nature Switzerland AG
- eBook ISBN
- 978-3-030-54430-0
- DOI
- 10.1007/978-3-030-54430-0
- Hardcover ISBN
- 978-3-030-54429-4
- Series ISSN
- 0743-1643
- Edition Number
- 1
- Number of Pages
- XXV, 283
- Topics
