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**11**

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**2**answers

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### What's an example of 2 elliptic curves with the same ground ring s.t. their associated cohomology theories detect different things?

My understanding is that a complex-oriented spectrum is a ring spectrum $E$ with a map $MU \to E$.
Analogously, a ring with a formal group law is a ring $R$ with a map $L \to R$ (where $L$ is the ...

**7**

votes

**1**answer

265 views

### Must we know $MU^*(X)$ in order to compute $Ell^*(X)$?

Let $Ell^*(X)$ be the elliptic cohomology theory (associated to a given elliptic curve $E$) of a nice space $X$.
Recall the Landweber-Ravenel-Stong construction:
$MU^*(X) \otimes_{MU^*} R \simeq ...

**6**

votes

**0**answers

242 views

### Twisted equivariant modular forms?

I'd like to know where I can find information about a class of objects which I think deserve to be called twisted equivariant modular forms. Let me guess a definition, indicate how it can be made more ...

**28**

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**2**answers

1k views

### What do loop groups and von Neumann algebras have to do with elliptic cohomology?

Recall that complex $K$-theory is a cohomology theory on topological spaces, which can be described in several equivalent ways:
Given a finite complex $X$, $K^0(X)$ is the Grothendieck group of ...

**15**

votes

**1**answer

412 views

### Character of parity-twisted supersymmetric VOA module — question inspired by the Stolz-Teichner program

I'll begin with some background that is unnecessary for the actual question, but that might be interesting to the reader:
Topological modular forms ($TMF$) is a generalized cohomology theory whose ...

**8**

votes

**2**answers

556 views

### Elliptic genus for manifolds with boundary

Let M be a closed spin manifold of dimension $d$. One form of the elliptic genus of $M$ is
$$ F(q)=q^{-d/8} \hat A(M) {\rm ch} \otimes_{k=1/2,3/2,\cdots} \Lambda_{q^k}T \otimes_{\ell=1}^\infty ...

**16**

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**2**answers

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### Virasoro action on the elliptic cohomology

I'm trying to understand better the mathematical notion of elliptic cohomology. Note that I only know the physics definition of the elliptic genus given in Witten's paper.
Let $X$ be a Calabi-Yau ...

**12**

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**3**answers

1k views

### complex cobordism from formal group laws?

Reading Ravenel's "green book", I wonder about his question on p.15 "that the spectrum MU may be constructed somehow using formal group law theory without using complex manifolds or vector bundles. ...

**19**

votes

**3**answers

2k views

### What is a TMF in topology?

What is a topological modular form? How are they related to 'normal' (number-theoretic) modular forms?