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petergreat
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If the first homology group of a manifold is Z^n, does it imply that the first homology group with real coefficients (obtained from singular chains with real coefficients) is R^n?
petergreat said:If the first homology group of a manifold is Z^n, does it imply that the first homology group with real coefficients (obtained from singular chains with real coefficients) is R^n?
Homology refers to the similarity between different organisms or structures that is due to shared ancestry. In other words, if two organisms or structures are homologous, it means they have a common evolutionary origin.
Homology is determined through comparative analysis of anatomical, genetic, and developmental features. If two organisms or structures share similar traits and patterns of development, they are likely to be homologous.
Homology and analogy are both terms used to describe similarity between organisms or structures. However, homology refers to similarity due to shared ancestry, while analogy refers to similarity due to convergent evolution.
Yes, homology can be observed at the molecular level through DNA and protein sequence analysis. Similarities in sequences between different species can indicate shared ancestry and homology.
Homology is important in evolutionary biology because it provides evidence for common ancestry and helps us understand the relationships between different species. It also allows us to make predictions about the evolutionary history of organisms and how they may have adapted to different environments.