Highly divisible cycles in homological Atiyah-Hirzebruch spectral sequences

Q: What type of study is this?

This is a Quantitative Study study.

Vasilii Rozhdestvenskii

doi:10.48550/arxiv.2507.09769

July 13, 2025Open Access

Highly divisible cycles in homological Atiyah-Hirzebruch spectral sequences

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Key Points

Maximal order elements were identified in the groups involved in the Atiyah-Hirzebruch spectral sequence.
The study specifically focuses on the structure of groups derived from the homology theory of finite type.
This work explores the relationship between homological groups and their finite type properties.
Results provide a framework for understanding cycles in the context of spectral sequences.

Implication

This analysis reveals elements with maximal order in the homology groups of CW-complexes, suggesting deeper insights into spectral sequences.

Abstract

Let F_* be a homology theory of finite type and ʳs,t(X)=Zʳs,t(X)Bʳs,t(X); dʳs,t\ denote the Atiyah-Hirzebruch spectral sequence for F_* of a $CW$-complex X. In this paper we study elements of the maximal possible order in the groups E²n,0(X)/Zʳn,0(X).

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Cite This Study

Vasilii Rozhdestvenskii (2025) studied this question.

synapsesocial.com/papers/68de5da783cbc991d0a20bd4 https://doi.org/10.48550/arxiv.2507.09769

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Highly divisible cycles in homological Atiyah-Hirzebruch spectral sequences

Key Points

Implication

Abstract

Discussion

Cite This Study

Highly divisible cycles in homological Atiyah-Hirzebruch spectral sequences

Key Points

Implication

Abstract

Discussion

Cite This Study

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