3,468 reputation
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bio website cwru.edu/artsci/phil/…
location Case Western Reserve University
age 63
visits member for 2 years, 9 months
seen 17 hours ago

2d
comment Example of torsion in orientable manifolds?
@JohnPardon I learned of lens spaces from Seifert and Threlfall when I first began learning of homology and I did not know what mattered about them so I did not retain much. They include $\mathbb{RP}^3$ and a quick introduction is map.mpim-bonn.mpg.de/Lens_spaces:_a_history
2d
comment Example of torsion in orientable manifolds?
@QiaochuYuan Yes. I can picture $\mathbb{RP}^3$. But let me check my picture: the torsion 2-cycle is the natural projective plane in $\mathbb{RP}^3$, right?
Jan
28
accepted Example of torsion in orientable manifolds?
Jan
28
asked Example of torsion in orientable manifolds?
Jan
27
comment Who first talked about “holes” in homology?
@paulgarrett I really appreciate this input, but I see that as Alexandroff uses the term "hole," there cannot be any holes in a closed surface (i.e. in a compact boundary-less surface). Homology certainly does not count holes in his sense.
Jan
27
revised Who first talked about “holes” in homology?
Notice that even Alexandroff does not say that torus, for example, has "holes".
Jan
27
revised Who first talked about “holes” in homology?
Added discussion of where the term is not used.
Jan
27
comment Who first talked about “holes” in homology?
@paulgarrett Also, we see what is going on around us. With a 1977 Princeton PhD you might well have heard Atiyah himself use the term. You certainly knew people who did.
Jan
27
awarded  Custodian
Jan
27
comment Who first talked about “holes” in homology?
@paulgarrett Nice call. That is a stunning book. But I think he only uses the term "hole" in passing and does not offer it as a general explanation of the genus of a surface or of homology groups.
Jan
27
reviewed Approve Help in understanding “Local well-posedness for the Maxwell-Schrodinger system”
Jan
27
comment Who first talked about “holes” in homology?
@AlexDegtyarev Then you really should read Atiyah's essay.
Jan
27
asked Who first talked about “holes” in homology?
Jan
9
comment What is known about global well ordering of classes in Gödel-Bernays?
A beautiful result. I fear it sinks my strategy for the problem that led to this question, but maybe that failure points the way to what will work.
Jan
9
accepted What is known about global well ordering of classes in Gödel-Bernays?
Jan
7
comment What is known about global well ordering of classes in Gödel-Bernays?
Terrific. I will take some time to absorb this. Since I really want this in a weak fragment of ZFC, the use of $Z_2$ is very encouraging.
Jan
7
comment What is known about global well ordering of classes in Gödel-Bernays?
@AsafKaragila I want well ordering not in classes, but of classes.
Jan
7
asked What is known about global well ordering of classes in Gödel-Bernays?
Dec
27
accepted What is the consistency strength of a standard model of ZF versus a transitive model?
Dec
27
comment What is the consistency strength of a standard model of ZF versus a transitive model?
@AndresCaicedo Compared to proof theory, I tend to think of set theory as having all settled terminology. I have clarified in the question.