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Hello,

I have very general , "introductory" questions (It is quite hard for me to seek for specific things in the algebraic topology literature).

I guess that connective spectra have a model structure. So do simplicial abelian groups. Are these Quillen equivalent?

Secondly, I think of a simplicial abelian group as a space with strictly associative and commutative multiplicationoperation, while I think of a connective spectrum as a space with multiplication an operation which is associative and commutative up to all higher coherences (i.e. some words like $E_{\infty}$). So these are similar. How do I see what extra richness is encoded in a spectrum? For example, what mental pictures do I lose when I think of a connective spectrum as a right-bounded chain complex?

I think that the last is the most important for me, to have some small mental picture which I should have for spectra but not for simplicial abelian groups / chain complexes.

Thank you, Sasha

2 Typos + added some tags

Hello,

I have very general , "introductory" questions (It is quite hard for me to seek for specific things in the algebraic topology literature).

I guess that connective spectrums spectra have a model structure. So do simplicial abelian groups. Are these Quillen equivalent?

Secondly, I think of a simplicial abelian group as a space with strictly ass. associative and comm. commutative multiplication, while I think of a connective spectrum as of a space with multiplication which is ass. associative and comm. commutative up to all higher coherences (i.e. some words like $E_{\infty}$). So these are similiarsimilar. How do I see what extra richness is encoded in a spectrum? for For example, what mental pictures do I lose when I think of a connective spectrum as a right-bounded chain complex?

I think that the last is the most important for me, to have some small mental picture which I should have for spectrums spectra but not for simplicial abelian groups / chain complexes.

Thank you, Sasha

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# Connective spectra versus simplicial abelian groups - very basic question

Hello,

I have very general , "introductory" questions (It is quite hard for me to seek for specific things in the algebraic topology literature).

I guess that connective spectrums have a model structure. So do simplicial abelian groups. Are these Quillen equivalent?

Secondly, I think of a simplicial abelian group as a space with strictly ass. and comm. multiplication, while of a connective spectrum as of a space with multiplication which is ass. and comm. up to all higher coherences (i.e. some words like $E_{\infty}$). So these are similiar. How do I see what extra richness is encoded in a spectrum? for example, what mental pictures do I lose when I think of a connective spectrum as a right-bounded chain complex?

I think that the last is the most important for me, to have some small mental picture which I should have for spectrums but not for simplicial abelian groups / chain complexes.

Thank you, Sasha