Cobordisms and Spectral Sequences

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Brand new. We distribute directly for the publisher. Cobordism is one of the most basic notions of algebraic topology. This book is devoted to spectral sequences related to ... cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and applications of these and other sequences to the investigation of cobordism rings. Read more Show Less

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Overview

Cobordism is one of the most basic notions of algebraic topology. This book is devoted to spectral sequences related to cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and applications of these and other sequences to the investigation of cobordism rings.

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Editorial Reviews

Booknews
Translated from the 1991 Russian edition. The author discusses the spectral sequences related with cobordism theory: the spectral sequence of a singularity, the Adams-Novikov spectral sequence, and others, and applications of these spectral sequences in the investigation of cobordism rings. Chapters describe bordism with singularities, quadrilateral spectral sequences, spectral sequences for MSp, symplectic cobordism with singularities, and orientability and splitting of spectra. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Table of Contents

Introduction 1
Ch. I Bordism with Singularities 7
1 Definition and general properties of bordism with singularities 7
2 Spectral sequence of a singularity 13
3 Multiplicative properties of the spectral sequence of a singularity 17
Ch. II Quadrilateral of Spectral Sequences 23
1 Adams-Novikov spectral sequence in categories 23
2 Properties of the Adams-Novikov spectral sequence 25
3 Construction of the quadrilateral of spectral sequences 33
4 Algebraic spectral sequences 37
5 Examples 47
Ch. III Spectral Sequences for MSp 51
1 Modified algebraic spectral sequence for MSp 51
2 First differential of the modified algebraic spectral sequence for MSp 54
3 Triple products of Ray elements 62
Ch. IV Symplectic Cobordism with Singularities 65
1 The theories [actual symbol not reproducible] 65
2 Cohomology of [actual symbol not reproducible] as modules over the Steenrod algebra 69
3 The theory [actual symbol not reproducible] 71
4 Symplectic cobordism with singularities in low dimensions 74
Ch. V Orientability and Splitting of Spectra 79
1 Ray elements as obstructions to orientability of symplectic cobordism 79
2 Splitting of spectra and of their cohomology 82
3 Spectral sequences of singularities and the spectrum BoP 87
Tables 91
References 95
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