On spherical classes in $H_*QX$

Hadi Zare

arXiv:1101.1215·math.AT·January 7, 2011·1 cites

On spherical classes in $H_*QX$

Hadi Zare

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TL;DR

This paper establishes an upper bound on spherical classes in the homology of infinite loop spaces for specific spaces, connecting to the Curtis conjecture and offering insights into bordism classes of immersions.

Contribution

It provides new bounds on spherical classes in $H_*QX$ for $X=P$ and $S^1$, advancing understanding related to the Curtis conjecture and bordism theory.

Findings

01

Upper bound on spherical classes in $H_*QX$ for $X=P,S^1$

02

Connections made to the Curtis conjecture on spherical classes

03

Insights into bordism classes of immersions for Thom complexes

Abstract

We give an upper bound on the set of spherical classes in $H_{*} QX$ when $X = P, S^{1}$ . This is related to the Curtis conjecture on spherical classes in $H_{*} Q_{0} S^{0}$ . The results also provide some control over the bordism classes on of immersions when $X$ is a Thom complex.

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Taxonomy

TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis