Classifying Immersions into ℝ4 over Stable Maps of 3-Manifolds into ℝ2

1985 ◽  
Author(s):  
Harold Levine
Keyword(s):  
Stable Maps

scholarly journals Invariants of Stable Maps between Closed Orientable Surfaces

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 215
Author(s):  
Catarina Mendes de Jesus S. ◽  
Pantaleón D. Romero
Keyword(s):  
Point Of View ◽  
Stable Maps ◽  
Smooth Maps ◽  
Orientable Surfaces

In this paper, we will consider the problem of constructing stable maps between two closed orientable surfaces M and N with a given branch set of curves immersed on N. We will study, from a global point of view, the behavior of its families in different isotopies classes on the space of smooth maps. The main goal is to obtain different relationships between invariants. We will provide a new proof of Quine’s Theorem.

Graphs of stable maps between closed orientable surfaces

2016 ◽  
Vol 36 (3) ◽  
pp. 1185-1194 ◽  
Author(s):  
C. Mendes de Jesus
Keyword(s):  
Stable Maps ◽  
Orientable Surfaces

scholarly journals Towards Mori’s program for the moduli space of stable maps

2011 ◽  
Vol 133 (5) ◽  
pp. 1389-1419 ◽  
Author(s):  
Dawei Chen ◽  
Izzet Coskun
Keyword(s):  
Moduli Space ◽  
Stable Maps

scholarly journals Universal Cohomological Expressions for Singularities in Families of Genus 0 Stable Maps

2017 ◽  
Vol 2018 (22) ◽  
pp. 6817-6843 ◽  
Author(s):  
Maxim Kazarian ◽  
Sergey Lando ◽  
Dimitri Zvonkine
Keyword(s):  
Stable Maps

Moduli Spaces of Stable Maps

2018 ◽  
pp. 213-220
Author(s):  
Maxim E. Kazaryan ◽  
Sergei K. Lando ◽  
Victor V. Prasolov
Keyword(s):  
Moduli Spaces ◽  
Stable Maps

scholarly journals CONSTRUCTED TWO-PARAMETER STRUCTURALLY STABLE MAPS

2019 ◽  
Vol 6 (438) ◽  
pp. 302-307
Author(s):  
Angisin Seitmuratov ◽  
◽  
Aigul Ospanovna Dauitbayeva ◽  
Kamalbek Berkimbayev ◽  
Nurzhanar Absamatovna Turlugulova ◽  
...  
Keyword(s):  
Stable Maps ◽  
Two Parameter ◽  
Structurally Stable

Modulation of microtubule dynamic instability in vivo by brain microtubule associated proteins

1995 ◽  
Vol 108 (4) ◽  
pp. 1679-1689 ◽  
Author(s):  
R. Dhamodharan ◽  
P. Wadsworth
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Instability ◽  
Average Rate ◽  
Stable Maps ◽  
Microtubule Dynamic ◽  
Unit Distance ◽  
Microtubule Associated Proteins ◽  
Heat Stable ◽  
Associated Proteins

Heat-stable brain microtubule associated proteins (MAPs) and purified microtubule associated protein 2 (MAP-2) were microinjected into cultured BSC-1 cells which had been previously injected with rhodamine-labeled tubulin. The dynamic instability behavior of individual microtubules was then examined using low-light-level fluorescence microscopy and quantitative microtubule tracking methods. Both MAP preparations suppressed microtubule dynamics in vivo, by reducing the average rate and extent of both growing and shortening events. The average duration of growing events was not affected. When measured as events/unit time, heat-stable MAPs and MAP-2 did not significantly alter the frequency of rescue; the frequency of catastrophe was decreased approximately two-fold by heat-stable MAPs and MAP-2. When transition frequencies were calculated as events/unit distance, both MAP preparations increased the frequency of rescue, without altering the frequency of catastrophe. The percentage of total time spent in the phases of growth, shrink and pause was determined. Both MAP-2 and heat-stable MAPs decreased the percentage of time spent shortening, increased the percentage of time spent paused, and had no effect on percentage of time spent growing. Heat-stable MAPs increased the average pause duration, decreased the average number of events per minute per microtubule and increased the probability that a paused microtubule would switch to growing rather than shortening. The results demonstrate that addition of MAPs to living cells reduces the dynamic behavior of individual microtubules primarily by suppressing the magnitude of dynamic events and increasing the time spent in pause, where no change in the microtubule length can be detected. The results further suggest that the expression of MAPs directly contributes to cell type-specific microtubule dynamic behavior.

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