Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Komplexe elliptische Geschlechter und S^1-aequivariante
  Kobordismustheorie (Complex elliptic genera and S^1-equivariant cobordism
  theory)   We introduce the universal complex elliptic genus phi_ell as the ring
homomorphism from the complex cobordism ring Omega^U to the polynomial ring
C[A,B,C,D] associated to the characteristic power series Q(x)=x/f(x), where f
is the solution of the differential equation (f'/f)'=S(f'/f), S(y) =
(y+A/2)^4-B/4*(y+A/2)^2+4C*(y+A/2)+B^2/64-2D. Formally, phi_ell arises as the
index of the Dolbeault operator of the loop space of a manifold. For manifolds
with vanishing first Chern class, phi_ell becomes a Jacobi form F(z,\tau) for
the full Jacobi group Z^2 x PSL_2(Z). We prove the rigidity of phi_ell for
S^1-actions on SU-manifolds. The kernel of phi_ell in the rational SU-cobordism
ring is characterized as the ideal generated by manifolds with S^1-action of
fixed type t (an integer) different from 0.
  For z to be an N-division point on the elliptic curve determined by \tau,
phi_ell specializes to the Level N genus phi_N. We introduce the cobordism ring
Omega^{U,N} of stably almost complex manifolds with first Chern class divisible
by N and characterize the kernel of phi_N by certain ideals in the rationalized
ring Omega^{U,N}.
  In Chapter 1, we construct a base sequence W_1, W_2, W_3, ... of the rational
cobordism ring Omega^U on which phi_ell has the values A, B, C, D, and 0 for
W_i with i>=5. In Chapter 2, phi_ell and phi_N are investigated and the main
results are proven. Chapter 3 contains the further result that the level N
genus is invariant under the blow up along a submanifold Y of a complex
manifold X if the codimension of Y in X is congruent 1 modulo N.

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: stat
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The categories of this paper are: physics