singular homology

奇异同调

Geometry & Topology · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

The homology of the free chain complex generated by continuous standard simplices in X, using alternating face boundaries; coefficients are integers unless stated otherwise.

由映入 $X$ 的连续标准单形生成的自由链复形的同调，边界取交错面和；默认系数为整数。

Example

$H_1(S^1;\mathbb Z)\cong\mathbb Z$ and $H_1(D^2;\mathbb Z)=0$.

Usage and distinctions

Ordinary homology has $H_0$ of a point equal to $\mathbb Z$; reduced homology of a point vanishes.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Allen Hatcher — Algebraic Topology§2.1, Singular Homology, printed pp. 108–110 · Checked 2026-10-14

Translation sources

1. Li Xiaobin — Southwest Jiaotong University, Gromov–Witten study guide§1.2 基础拓扑学，核心内容：奇异同调 · Checked 2026-10-14

Original encyclopedia and terminology content: CC BY-SA 4.0. Contribute or report a correction.