Combinatorial topology

In mathematics, combinatorial topology was an older name for algebraic topology, dating from the time when topological invariants of spaces (for example the Betti numbers) were regarded as derived from combinatorial decompositions such as simplicial complexes.

The change of name reflected the move to organise topological classes such as cycles modulo boundaries explicitly into abelian groups. This point of view is often attributed to Emmy Noether, and so the change of title may reflect her influence.



In the News

Early Warning Signs Of Alzheimer's Show Up Across Cognitive Areas Year
By combing through dozens of Alzheimer's disease (AD) studies, psychologists have gained a clear picture of cognitive problems in people who will develop the degenerative brain disease. The meta-analysis reveals that people can show early warning signs across several cognitive domains years before they are officially diagnosed, confirming that Alzheimer's causes general deterioration and tends to follow a stable preclinical stage with a sharp drop in function.

Genetic Background To Severe Urinary Tract Infections
If you sit on cold boulders or forget to wear your woollen pants, you can develop a urinary tract infection, or so the story goes. It turns out though, that these diseases are more complicated than this, and in some cases they have a genetic background. Scientists have found a gene that appears to lie behind many of the most severe urinary tract infections.

Scientists Regenerate Wing In Chick Embryo
Chop off a salamander's leg and a brand new one will sprout in no time. But most animals have lost the ability to replace missing limbs. Now, a research team at the Salk Institute for Biological Studies has been able to regenerate a wing in a chick embryo -- a species not known to be able to regrow limbs -- suggesting that the potential for such regeneration exists innately in all vertebrates, including humans.

'Marital Strain' Increases Women's Risk Of Death, Heart Disease
Married women who avoid conflict with their spouses have an increased risk of dying from any cause, researchers report today at the Second International Conference on Women, Heart Disease and Stroke.

The Planetary Society: Cosmos 1: The First Solar Sail
Details about the June 2005 mission of the Cosmos 1 solar sail spacecraft, which is "a spacecraft without an engine —it is pushed along directly by light particles from the Sun, reflecting off giant mirror-like sails."Feature background information about this Russian-built spacecraft, images and animations, instructions for building a scale model of the craft, a blog, and other information related to the privately funded Cosmos 1 mission. From The Planetary Society.

[Ironic] An Italian pensioner committed suicide after his wife fell in
Recalling the end of Romeo and Juliet, the 70-year-old man, Ettore, who had sat by his wife's bedside for four months after she slipped into a coma following a heart attack, finally gave up hope and gassed himself in the garage of his family home.Less than a day later, his wife, Rossana, woke up in her hospital bed in Padua and immediately asked for him.

New Genome Comparison Finds Chimps, Humans Very Similar at the DNA Lev
Summary of the results of the "first comprehensive comparison of the genetic blueprints of humans and chimpanzees [which] shows our closest living relatives share perfect identity with 96 percent of our DNA sequence."Includes the full text of the report by the Chimpanzee Sequencing and Analysis Consortium, published in the journal Nature. From the National Human Genome Research Institute (NHGRI), National Institutes of Health (NIH).

[Scary] Pregnant woman says 'maternal instinct' helped her kill attack
FORT MITCHELL, Ky. - A pregnant woman who killed her attacker said a maternal instinct helped her fight off the woman who investigators believe was after her unborn child."I do believe that I fought harder because it was for my child,"Sarah Brady told ABC's "Good Morning America"in interviews aired Sunday and Monday. "It is a maternal instinct to protect your child to the very end."Katherine Smith, 22, died Thursday after luring Brady to her apartment to pick up a package supposedly delivered to the wrong address. When Smith pulled out a knife and attacked the pregnant woman, Brady fought back, striking Smith on the head with an ash tray and stabbing her three times with her own knife, police said. Brady, 26, said she didn't know Smith before the two met at Smith's apartment and can't be certain why Smith wanted to kill her."I really am not sure what was going through her mind,"Brady told ABC. "The only thing I thought was that she was going to kill me and my child and that is the only thing that ran through my mind."

National Lab Researchers Develop Impurity-free Process For Powder Inje
Researchers at the Department of Energy's Pacific Northwest National Laboratory have developed a new method for powder injection molding of titanium and similar materials to form components for advanced engineering applications.

Natural Protection Provides Possible New Treatments For Stroke
Two substances that occur naturally in the brain act to protect the brain during a stroke. This is the conclusion of a dissertation published at the Sahlgrenska Academy, and the discovery may lead to new treatmentsfor stroke patients. Stroke is the result of an infarction, or bleeding, within the brain, and it may lead to impaired movement, impaired sensation, and difficulties in cognitive function and speech. Approximately 30,000 people are affected by stroke each year in Sweden, and it is the most common cause of long-term dependence on care.


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