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On rigidity of complex Hirzebruch genera on $SU$-manifolds

Georgy Chernykh

Abstract

We prove that if a complex genus $\varphi \colon \varOmega^U \to R$ is rigid on $SU$-manifolds with a torus action then $\varphi$ is the elliptic Krichever genus.

On rigidity of complex Hirzebruch genera on $SU$-manifolds

Abstract

We prove that if a complex genus is rigid on -manifolds with a torus action then is the elliptic Krichever genus.
Paper Structure (2 sections, 6 theorems, 45 equations)

This paper contains 2 sections, 6 theorems, 45 equations.

Table of Contents

  1. Preliminaries
  2. Main result

Key Result

Theorem 1.1

Let $\varphi \colon \varOmega^U \to R$ be a complex genus with the exponent $f(x)=x+\ldots \in R[[x]]$, and let $M$ be a stably complex $2n$-dimensional $T^k$-manifold with isolated fixed points $M^T$. Then the equivariant genus $\varphi^T ([M]) = \varphi([M]) + \ldots$ is given by where $\langle w, x \rangle = w_1x_1 + \ldots + w_kx_k$ for $w = (w_1,\ldots,w_k)$.

Theorems & Definitions (8)

  • Theorem 1.1: bu-pa-ra10 or bu-pa15
  • Remark
  • Theorem 1.2: kr90
  • Theorem 1.3: bu-pa-ra10 or bu-pa15
  • Theorem 2.1: bu-pa15
  • Theorem 2.2
  • Corollary 2.3
  • proof : Proof of Theorem \ref{['main']}