Why there isn't any mention of topology

• MathematicalPhysicist
In summary, the name differential geometry and tensor analysis is a bit of a confusing title, and there may be better names for the areas it covers. There has been discussion about changing the name recently, but nothing has been decided yet. Most of the forum users are university/college students, and it seems that they would not be interested in posts about high school geometry.
MathematicalPhysicist
Gold Member
in the title of differential geometry and tensor analysis?
such a crucial topic in maths should have its name mentioned should it not?

It will come around soon enough.

The name would probably be too long.

so perhaps we need an all encompassing name for those areas?
I mean obviously algebraic topology,geometric topology, differential geometry have a lot to do with geometry, so perhaps a name such as: geometry & topology will do?

I guess part of the current title is meant to get people who are interested in mathematical aspects of General Relativity...particularly Tensors [which is probably why it is distinguished there]. While an expert would appreciate the title "geometry & topology"... the novice probably won't. With that title, one might get lots of questions about high-school geometry. Maybe "Advanced Geometry & Topology"... but one might need to throw in "Tensors".

I'm pretty sure the word topology was in the forum title not that long ago, unless I'm terribly mistaken.

Nothing seems to have changed since then though.

I really don't understand why the TA&DG is so-named. Surely topology warrants more attention than "tensor analysis" - whatever this means?

morphism said:

Nothing seems to have changed since then though.

I really don't understand why the TA&DG is so-named. Surely topology warrants more attention than "tensor analysis" - whatever this means?

Ahh right. Thats where I remember the topology from.

robphy said:
I guess part of the current title is meant to get people who are interested in mathematical aspects of General Relativity...particularly Tensors [which is probably why it is distinguished there]. While an expert would appreciate the title "geometry & topology"... the novice probably won't. With that title, one might get lots of questions about high-school geometry. Maybe "Advanced Geometry & Topology"... but one might need to throw in "Tensors".
sorry, rob, but that's rubbish, I don't recall learning topology in high school, and I'm no expert in topology or geometry but an undergraduate student who learns this stuff, and I don't see how high schooler can choose to post at a forum where he sees all posts in subjects unfamiliar to him.
anyway, most of the users are university/college students aren't they?
that's my feeling from the forum discussing university life here, forgot the name of the forum.

1. Why isn't topology mentioned in this research study?

There could be several reasons for this. The study may not be directly related to topology, so it was not included in the discussion. Alternatively, topology may not be relevant to the specific research question being addressed. Additionally, the study may be limited in scope and did not have the resources to include a discussion on topology.

2. How does topology relate to this scientific topic?

Topology is the study of the properties of a geometric figure that are preserved under continuous deformations, such as stretching or bending. In many scientific fields, topology can provide valuable insights into the structure and behavior of complex systems. For example, in biology, topology can help understand the shape and function of proteins, while in physics, it can explain the behavior of quantum particles.

3. Is topology a commonly used concept in scientific research?

It depends on the specific field of study. In some areas, such as mathematics, topology is a fundamental concept and is used extensively. In other fields, its relevance may vary. However, with the growing complexity of scientific research, topology is becoming increasingly important in understanding and analyzing complex systems.

4. Are there any current developments in topology that may be relevant to this topic?

Topology is a rapidly evolving field, and new developments are continuously being made. It is possible that there may be recent studies or theories in topology that could shed light on the topic at hand. It is always recommended to stay updated on current research and advancements in related fields.

5. How can topology be applied to real-world problems?

Topology has numerous applications in various fields, including physics, biology, computer science, and engineering. It can be used to model and analyze complex systems, understand network structures, and make predictions about the behavior of these systems. Additionally, topology can also be applied in data analysis, optimization, and machine learning.

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