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.
Author(s): V. V. Vershinin
Series: Translations of Mathematical Monographs 130
Publisher: American Mathematical Society
Year: 1993
Language: English
Pages: 106
Introduction 1
Chapter 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
Chapter 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
Chapter 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
Chapter IV. Symplectic Cobordism with Singularities 65
1. The theories MSp;n(.) and MSp;(.) 65
2. Cohomology of MSpn and MSp as modules over the Steenrod algebra 69
3. The theory MSp* (.) 71
4. Symplectic cobordism with singularities in low dimensions 74
Chapter 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
